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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 9338.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9338.b1 | 9338a2 | \([1, -1, 0, -232, 174]\) | \(1384331873625/795308122\) | \(795308122\) | \([2]\) | \(3328\) | \(0.39748\) | |
9338.b2 | 9338a1 | \([1, -1, 0, 58, 0]\) | \(21369234375/12456892\) | \(-12456892\) | \([2]\) | \(1664\) | \(0.050911\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9338.b have rank \(2\).
Complex multiplication
The elliptic curves in class 9338.b do not have complex multiplication.Modular form 9338.2.a.b
sage: E.q_eigenform(10)
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.