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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 7260.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7260.p1 | 7260p4 | \([0, 1, 0, -188316, 17023620]\) | \(1628514404944/664335375\) | \(301289124165216000\) | \([2]\) | \(103680\) | \(2.0516\) | |
| 7260.p2 | 7260p2 | \([0, 1, 0, -86676, -9849996]\) | \(158792223184/16335\) | \(7408242927360\) | \([2]\) | \(34560\) | \(1.5022\) | |
| 7260.p3 | 7260p1 | \([0, 1, 0, -5001, -179676]\) | \(-488095744/200475\) | \(-5682459063600\) | \([2]\) | \(17280\) | \(1.1557\) | \(\Gamma_0(N)\)-optimal |
| 7260.p4 | 7260p3 | \([0, 1, 0, 38559, 1959120]\) | \(223673040896/187171875\) | \(-5305382304750000\) | \([2]\) | \(51840\) | \(1.7050\) |
Rank
sage: E.rank()
The elliptic curves in class 7260.p have rank \(0\).
Complex multiplication
The elliptic curves in class 7260.p do not have complex multiplication.Modular form 7260.2.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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
