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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 77616.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 77616.p1 | 77616fp1 | \([0, 0, 0, -1659, -38486]\) | \(-3451273/2376\) | \(-347640201216\) | \([]\) | \(82944\) | \(0.91486\) | \(\Gamma_0(N)\)-optimal |
| 77616.p2 | 77616fp2 | \([0, 0, 0, 13461, 575386]\) | \(1843623047/2044416\) | \(-299125079801856\) | \([]\) | \(248832\) | \(1.4642\) |
Rank
sage: E.rank()
The elliptic curves in class 77616.p have rank \(0\).
Complex multiplication
The elliptic curves in class 77616.p do not have complex multiplication.Modular form 77616.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
