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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 6240c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6240.e3 | 6240c1 | \([0, -1, 0, -46, -80]\) | \(171879616/38025\) | \(2433600\) | \([2, 2]\) | \(1024\) | \(-0.061236\) | \(\Gamma_0(N)\)-optimal |
| 6240.e1 | 6240c2 | \([0, -1, 0, -696, -6840]\) | \(72929847752/5265\) | \(2695680\) | \([2]\) | \(2048\) | \(0.28534\) | |
| 6240.e2 | 6240c3 | \([0, -1, 0, -241, 1441]\) | \(379503424/24375\) | \(99840000\) | \([2]\) | \(2048\) | \(0.28534\) | |
| 6240.e4 | 6240c4 | \([0, -1, 0, 104, -620]\) | \(240641848/428415\) | \(-219348480\) | \([2]\) | \(2048\) | \(0.28534\) |
Rank
sage: E.rank()
The elliptic curves in class 6240c have rank \(0\).
Complex multiplication
The elliptic curves in class 6240c do not have complex multiplication.Modular form 6240.2.a.c
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
