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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 2646.q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2646.q1 | 2646v3 | \([1, -1, 1, -62264, 5995567]\) | \(-11527859979/28\) | \(-64839187476\) | \([]\) | \(10368\) | \(1.3149\) | |
| 2646.q2 | 2646v1 | \([1, -1, 1, -524, 13647]\) | \(-5000211/21952\) | \(-69731032896\) | \([]\) | \(3456\) | \(0.76559\) | \(\Gamma_0(N)\)-optimal |
| 2646.q3 | 2646v2 | \([1, -1, 1, 4621, -327981]\) | \(381790581/1835008\) | \(-52460506054656\) | \([]\) | \(10368\) | \(1.3149\) |
Rank
sage: E.rank()
The elliptic curves in class 2646.q have rank \(1\).
Complex multiplication
The elliptic curves in class 2646.q do not have complex multiplication.Modular form 2646.2.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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
