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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 93925.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
93925.q1 | 93925i1 | \([1, 0, 1, -7376, 51273]\) | \(117649/65\) | \(24514718515625\) | \([2]\) | \(245760\) | \(1.2597\) | \(\Gamma_0(N)\)-optimal |
93925.q2 | 93925i2 | \([1, 0, 1, 28749, 412523]\) | \(6967871/4225\) | \(-1593456703515625\) | \([2]\) | \(491520\) | \(1.6063\) |
Rank
sage: E.rank()
The elliptic curves in class 93925.q have rank \(2\).
Complex multiplication
The elliptic curves in class 93925.q do not have complex multiplication.Modular form 93925.2.a.q
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.