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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 17325.t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 17325.t1 | 17325bg3 | \([1, -1, 1, -198230, -33920728]\) | \(75627935783569/396165\) | \(4512566953125\) | \([2]\) | \(73728\) | \(1.6242\) | |
| 17325.t2 | 17325bg2 | \([1, -1, 1, -12605, -508228]\) | \(19443408769/1334025\) | \(15195378515625\) | \([2, 2]\) | \(36864\) | \(1.2776\) | |
| 17325.t3 | 17325bg1 | \([1, -1, 1, -2480, 38522]\) | \(148035889/31185\) | \(355216640625\) | \([2]\) | \(18432\) | \(0.93102\) | \(\Gamma_0(N)\)-optimal |
| 17325.t4 | 17325bg4 | \([1, -1, 1, 11020, -2209228]\) | \(12994449551/192163125\) | \(-2188858095703125\) | \([2]\) | \(73728\) | \(1.6242\) |
Rank
sage: E.rank()
The elliptic curves in class 17325.t have rank \(0\).
Complex multiplication
The elliptic curves in class 17325.t do not have complex multiplication.Modular form 17325.2.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.
