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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 7360.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7360.p1 | 7360t3 | \([0, 0, 0, -1772, -17136]\) | \(18778674312/6996025\) | \(229245747200\) | \([2]\) | \(5632\) | \(0.87971\) | |
| 7360.p2 | 7360t2 | \([0, 0, 0, -772, 8064]\) | \(12422690496/330625\) | \(1354240000\) | \([2, 2]\) | \(2816\) | \(0.53313\) | |
| 7360.p3 | 7360t1 | \([0, 0, 0, -767, 8176]\) | \(779704121664/575\) | \(36800\) | \([2]\) | \(1408\) | \(0.18656\) | \(\Gamma_0(N)\)-optimal |
| 7360.p4 | 7360t4 | \([0, 0, 0, 148, 26096]\) | \(10941048/8984375\) | \(-294400000000\) | \([4]\) | \(5632\) | \(0.87971\) |
Rank
sage: E.rank()
The elliptic curves in class 7360.p have rank \(1\).
Complex multiplication
The elliptic curves in class 7360.p do not have complex multiplication.Modular form 7360.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
