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Properties

Label 235950.in
Number of curves $2$
Conductor $235950$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("in1")
 
E.isogeny_class()
 

Elliptic curves in class 235950.in

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
235950.in1 235950in2 \([1, 0, 0, -48801541588, 4149521294522792]\) \(464352938845529653759213009/2445173327025000\) \(67683964131214625390625000\) \([2]\) \(464486400\) \(4.5732\)  
235950.in2 235950in1 \([1, 0, 0, -3048416588, 64911060147792]\) \(-113180217375258301213009/260161419375000000\) \(-7201434754209287109375000000\) \([2]\) \(232243200\) \(4.2266\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 235950.2.a.in

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{6} + 2 q^{7} + q^{8} + q^{9} + q^{12} - q^{13} + 2 q^{14} + q^{16} - 4 q^{17} + q^{18} + 2 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

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 LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.