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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 74025.q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 74025.q1 | 74025b1 | \([0, 0, 1, -780, 8386]\) | \(-77750599680/16121\) | \(-10881675\) | \([]\) | \(23616\) | \(0.34687\) | \(\Gamma_0(N)\)-optimal |
| 74025.q2 | 74025b2 | \([0, 0, 1, 270, 28721]\) | \(4423680/726761\) | \(-357620919075\) | \([]\) | \(70848\) | \(0.89618\) |
Rank
sage: E.rank()
The elliptic curves in class 74025.q have rank \(2\).
Complex multiplication
The elliptic curves in class 74025.q do not have complex multiplication.Modular form 74025.2.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.
