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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 7616.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7616.f1 | 7616e3 | \([0, 0, 0, -33836, -2394576]\) | \(16342588257633/8185058\) | \(2145663844352\) | \([2]\) | \(12288\) | \(1.3188\) | |
| 7616.f2 | 7616e2 | \([0, 0, 0, -2476, -23760]\) | \(6403769793/2775556\) | \(727595352064\) | \([2, 2]\) | \(6144\) | \(0.97228\) | |
| 7616.f3 | 7616e1 | \([0, 0, 0, -1196, 15664]\) | \(721734273/13328\) | \(3493855232\) | \([2]\) | \(3072\) | \(0.62570\) | \(\Gamma_0(N)\)-optimal |
| 7616.f4 | 7616e4 | \([0, 0, 0, 8404, -176080]\) | \(250404380127/196003234\) | \(-51381071773696\) | \([4]\) | \(12288\) | \(1.3188\) |
Rank
sage: E.rank()
The elliptic curves in class 7616.f have rank \(1\).
Complex multiplication
The elliptic curves in class 7616.f do not have complex multiplication.Modular form 7616.2.a.f
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
