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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 4830.t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4830.t1 | 4830s3 | \([1, 1, 1, -98216, 11806409]\) | \(104778147797811105409/289854482400\) | \(289854482400\) | \([2]\) | \(20480\) | \(1.4321\) | |
| 4830.t2 | 4830s2 | \([1, 1, 1, -6216, 177609]\) | \(26562019806177409/1343744640000\) | \(1343744640000\) | \([2, 2]\) | \(10240\) | \(1.0856\) | |
| 4830.t3 | 4830s1 | \([1, 1, 1, -1096, -10807]\) | \(145606291302529/37984665600\) | \(37984665600\) | \([2]\) | \(5120\) | \(0.73899\) | \(\Gamma_0(N)\)-optimal |
| 4830.t4 | 4830s4 | \([1, 1, 1, 3864, 709833]\) | \(6380108151242111/220374787500000\) | \(-220374787500000\) | \([2]\) | \(20480\) | \(1.4321\) |
Rank
sage: E.rank()
The elliptic curves in class 4830.t have rank \(1\).
Complex multiplication
The elliptic curves in class 4830.t do not have complex multiplication.Modular form 4830.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
