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Properties

Label 7293.a
Number of curves $2$
Conductor $7293$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 7293.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7293.a1 7293b1 \([1, 1, 1, -418941653, 704412075314]\) \(8131755985964161964448308988625/4491414222168968491132426977\) \(4491414222168968491132426977\) \([2]\) \(2956800\) \(3.9965\) \(\Gamma_0(N)\)-optimal
7293.a2 7293b2 \([1, 1, 1, 1632751712, 5569387382402]\) \(481375691534989591168533139109375/291970430882721534414299079537\) \(-291970430882721534414299079537\) \([2]\) \(5913600\) \(4.3431\)  

Rank

sage: E.rank()
 

The elliptic curves in class 7293.a have rank \(1\).

Complex multiplication

The elliptic curves in class 7293.a do not have complex multiplication.

Modular form 7293.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} - q^{4} + q^{6} + 3 q^{8} + q^{9} + q^{11} + q^{12} + q^{13} - q^{16} - q^{17} - q^{18} + 6 q^{19} + O(q^{20})\) 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 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.