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SageMath
E = EllipticCurve("ca1")
E.isogeny_class()
Elliptic curves in class 4800.ca
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4800.ca1 | 4800cc3 | \([0, 1, 0, -5633, -163137]\) | \(38614472/405\) | \(207360000000\) | \([2]\) | \(6144\) | \(0.98802\) | |
| 4800.ca2 | 4800cc2 | \([0, 1, 0, -633, 1863]\) | \(438976/225\) | \(14400000000\) | \([2, 2]\) | \(3072\) | \(0.64145\) | |
| 4800.ca3 | 4800cc1 | \([0, 1, 0, -508, 4238]\) | \(14526784/15\) | \(15000000\) | \([2]\) | \(1536\) | \(0.29488\) | \(\Gamma_0(N)\)-optimal |
| 4800.ca4 | 4800cc4 | \([0, 1, 0, 2367, 16863]\) | \(2863288/1875\) | \(-960000000000\) | \([2]\) | \(6144\) | \(0.98802\) |
Rank
sage: E.rank()
The elliptic curves in class 4800.ca have rank \(1\).
Complex multiplication
The elliptic curves in class 4800.ca do not have complex multiplication.Modular form 4800.2.a.ca
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.
