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Properties

Label 270400.fy
Number of curves $2$
Conductor $270400$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("fy1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 270400.fy have rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(5\)\(1\)
\(13\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(3\) \( 1 + 3 T^{2}\) 1.3.a
\(7\) \( 1 - 3 T + 7 T^{2}\) 1.7.ad
\(11\) \( 1 - 3 T + 11 T^{2}\) 1.11.ad
\(17\) \( 1 - 4 T + 17 T^{2}\) 1.17.ae
\(19\) \( 1 + 7 T + 19 T^{2}\) 1.19.h
\(23\) \( 1 - 4 T + 23 T^{2}\) 1.23.ae
\(29\) \( 1 - 8 T + 29 T^{2}\) 1.29.ai
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 270400.fy do not have complex multiplication.

Modular form 270400.2.a.fy

Copy content sage:E.q_eigenform(10)
 
\(q + 3 q^{7} - 3 q^{9} + 3 q^{11} + 4 q^{17} - 7 q^{19} + O(q^{20})\) 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 LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 270400.fy

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
270400.fy1 270400fy2 \([0, 0, 0, -123082700, -568122906000]\) \(-1762712152495281/171798691840\) \(-20098017024582615040000000\) \([]\) \(54190080\) \(3.5962\)  
270400.fy2 270400fy1 \([0, 0, 0, -1402700, 1042054000]\) \(-2609064081/2500000\) \(-292464640000000000000\) \([]\) \(7741440\) \(2.6233\) \(\Gamma_0(N)\)-optimal