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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 7440p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7440.m2 | 7440p1 | \([0, -1, 0, 7480, 91632]\) | \(11298232190519/7472736000\) | \(-30608326656000\) | \([2]\) | \(23040\) | \(1.2765\) | \(\Gamma_0(N)\)-optimal |
| 7440.m1 | 7440p2 | \([0, -1, 0, -32200, 790000]\) | \(901456690969801/457629750000\) | \(1874451456000000\) | \([2]\) | \(46080\) | \(1.6231\) |
Rank
sage: E.rank()
The elliptic curves in class 7440p have rank \(0\).
Complex multiplication
The elliptic curves in class 7440p do not have complex multiplication.Modular form 7440.2.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 Cremona 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 Cremona labels.
