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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 6930.t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6930.t1 | 6930z4 | \([1, -1, 1, -85838, 9686567]\) | \(95946737295893401/168104301750\) | \(122548035975750\) | \([2]\) | \(49152\) | \(1.5967\) | |
6930.t2 | 6930z3 | \([1, -1, 1, -69458, -6987769]\) | \(50834334659676121/338378906250\) | \(246678222656250\) | \([2]\) | \(49152\) | \(1.5967\) | |
6930.t3 | 6930z2 | \([1, -1, 1, -7088, 47567]\) | \(54014438633401/30015562500\) | \(21881345062500\) | \([2, 2]\) | \(24576\) | \(1.2501\) | |
6930.t4 | 6930z1 | \([1, -1, 1, 1732, 5231]\) | \(788632918919/475398000\) | \(-346565142000\) | \([2]\) | \(12288\) | \(0.90353\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 6930.t have rank \(0\).
Complex multiplication
The elliptic curves in class 6930.t do not have complex multiplication.Modular form 6930.2.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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.