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Properties

Label 235950eu
Number of curves $4$
Conductor $235950$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("eu1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 235950eu have rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1 - T\)
\(3\)\(1 + T\)
\(5\)\(1\)
\(11\)\(1\)
\(13\)\(1 - T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(7\) \( 1 + 4 T + 7 T^{2}\) 1.7.e
\(17\) \( 1 + 17 T^{2}\) 1.17.a
\(19\) \( 1 + 2 T + 19 T^{2}\) 1.19.c
\(23\) \( 1 + 6 T + 23 T^{2}\) 1.23.g
\(29\) \( 1 + 6 T + 29 T^{2}\) 1.29.g
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 235950eu do not have complex multiplication.

Modular form 235950.2.a.eu

Copy content sage:E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{6} - 4 q^{7} + q^{8} + q^{9} - q^{12} + q^{13} - 4 q^{14} + q^{16} + q^{18} - 2 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

Copy content sage:E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

Copy content sage:E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.

Elliptic curves in class 235950eu

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
235950.eu4 235950eu1 \([1, 1, 1, 2669347662, 983737078772031]\) \(75991146714893572533071/15147028085515223040000\) \(-419279440971928656936960000000000\) \([2]\) \(1161216000\) \(4.9389\) \(\Gamma_0(N)\)-optimal
235950.eu3 235950eu2 \([1, 1, 1, -133625052338, 18258779689972031]\) \(9532597152396244075685450929/313550122650789880627200\) \(8679268263021187058028172800000000\) \([2]\) \(2322432000\) \(5.2855\)  
235950.eu2 235950eu3 \([1, 1, 1, -671012188338, 211600476463604031]\) \(-1207087636168285491836819264689/236446260657750000000000\) \(-6544983968392253871093750000000000\) \([2]\) \(3483648000\) \(5.4882\)  
235950.eu1 235950eu4 \([1, 1, 1, -10736699688338, 13541107279713604031]\) \(4944928228995290413834018379264689/189679641808585500000\) \(5250453998782180265085937500000\) \([2]\) \(6967296000\) \(5.8348\)