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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 80688.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 80688.p1 | 80688b2 | \([0, -1, 0, -3147392, 2120788512]\) | \(5142706/81\) | \(54308734332745402368\) | \([2]\) | \(2728960\) | \(2.5874\) | |
| 80688.p2 | 80688b1 | \([0, -1, 0, -390552, -42779520]\) | \(19652/9\) | \(3017151907374744576\) | \([2]\) | \(1364480\) | \(2.2408\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 80688.p have rank \(1\).
Complex multiplication
The elliptic curves in class 80688.p do not have complex multiplication.Modular form 80688.2.a.p
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.
