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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 88445.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
88445.q1 | 88445bq1 | \([0, 1, 1, -99395, 12028356]\) | \(-47109013504/475\) | \(-1094992880275\) | \([]\) | \(311040\) | \(1.4691\) | \(\Gamma_0(N)\)-optimal |
88445.q2 | 88445bq2 | \([0, 1, 1, -48855, 24256509]\) | \(-5594251264/107171875\) | \(-247057768612046875\) | \([]\) | \(933120\) | \(2.0184\) |
Rank
sage: E.rank()
The elliptic curves in class 88445.q have rank \(2\).
Complex multiplication
The elliptic curves in class 88445.q do not have complex multiplication.Modular form 88445.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.