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Properties

Label 402930ba
Number of curves $2$
Conductor $402930$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("ba1")
 
E.isogeny_class()
 

Elliptic curves in class 402930ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
402930.ba1 402930ba1 \([1, -1, 0, -19953225, -34245908339]\) \(680266970173241641/1259462476800\) \(1626555446944605619200\) \([2]\) \(44236800\) \(2.9609\) \(\Gamma_0(N)\)-optimal
402930.ba2 402930ba2 \([1, -1, 0, -13506345, -56759702675]\) \(-210985985036261161/955686297060000\) \(-1234238241065208871140000\) \([2]\) \(88473600\) \(3.3075\)  

Rank

sage: E.rank()
 

The elliptic curves in class 402930ba have rank \(1\).

Complex multiplication

The elliptic curves in class 402930ba do not have complex multiplication.

Modular form 402930.2.a.ba

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} + 2 q^{7} - q^{8} + q^{10} + 6 q^{13} - 2 q^{14} + q^{16} + 6 q^{17} + 6 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.