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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 858.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 858.f1 | 858h4 | \([1, 1, 1, -41184, 3199767]\) | \(7725203825376001537/7722\) | \(7722\) | \([2]\) | \(1152\) | \(0.93427\) | |
| 858.f2 | 858h3 | \([1, 1, 1, -2684, 44615]\) | \(2138362647385537/333926700822\) | \(333926700822\) | \([2]\) | \(1152\) | \(0.93427\) | |
| 858.f3 | 858h2 | \([1, 1, 1, -2574, 49191]\) | \(1886079023633377/59629284\) | \(59629284\) | \([2, 2]\) | \(576\) | \(0.58769\) | |
| 858.f4 | 858h1 | \([1, 1, 1, -154, 791]\) | \(-404075127457/82223856\) | \(-82223856\) | \([4]\) | \(288\) | \(0.24112\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 858.f have rank \(0\).
Complex multiplication
The elliptic curves in class 858.f do not have complex multiplication.Modular form 858.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
