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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 98192.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 98192.f1 | 98192q4 | \([0, 1, 0, -652808, -140506508]\) | \(159661140625/48275138\) | \(9302615644596543488\) | \([2]\) | \(1990656\) | \(2.3449\) | |
| 98192.f2 | 98192q3 | \([0, 1, 0, -595048, -176849100]\) | \(120920208625/19652\) | \(3786938996375552\) | \([2]\) | \(995328\) | \(1.9983\) | |
| 98192.f3 | 98192q2 | \([0, 1, 0, -248488, 47583156]\) | \(8805624625/2312\) | \(445522234867712\) | \([2]\) | \(663552\) | \(1.7955\) | |
| 98192.f4 | 98192q1 | \([0, 1, 0, -17448, 543412]\) | \(3048625/1088\) | \(209657522290688\) | \([2]\) | \(331776\) | \(1.4490\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 98192.f have rank \(1\).
Complex multiplication
The elliptic curves in class 98192.f do not have complex multiplication.Modular form 98192.2.a.f
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
