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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 3330t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3330.w3 | 3330t1 | \([1, -1, 1, -47, -89]\) | \(15438249/2960\) | \(2157840\) | \([2]\) | \(512\) | \(-0.067330\) | \(\Gamma_0(N)\)-optimal |
| 3330.w2 | 3330t2 | \([1, -1, 1, -227, 1279]\) | \(1767172329/136900\) | \(99800100\) | \([2, 2]\) | \(1024\) | \(0.27924\) | |
| 3330.w1 | 3330t3 | \([1, -1, 1, -3557, 82531]\) | \(6825481747209/46250\) | \(33716250\) | \([2]\) | \(2048\) | \(0.62582\) | |
| 3330.w4 | 3330t4 | \([1, -1, 1, 223, 5419]\) | \(1689410871/18741610\) | \(-13662633690\) | \([2]\) | \(2048\) | \(0.62582\) |
Rank
sage: E.rank()
The elliptic curves in class 3330t have rank \(0\).
Complex multiplication
The elliptic curves in class 3330t do not have complex multiplication.Modular form 3330.2.a.t
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
