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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 6930.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6930.f1 | 6930h4 | \([1, -1, 0, -31680, 2166426]\) | \(4823468134087681/30382271150\) | \(22148675668350\) | \([6]\) | \(27648\) | \(1.3981\) | |
| 6930.f2 | 6930h2 | \([1, -1, 0, -2430, -43524]\) | \(2177286259681/105875000\) | \(77182875000\) | \([2]\) | \(9216\) | \(0.84882\) | |
| 6930.f3 | 6930h3 | \([1, -1, 0, -810, 73440]\) | \(-80677568161/3131816380\) | \(-2283094141020\) | \([6]\) | \(13824\) | \(1.0515\) | |
| 6930.f4 | 6930h1 | \([1, -1, 0, 90, -2700]\) | \(109902239/4312000\) | \(-3143448000\) | \([2]\) | \(4608\) | \(0.50224\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 6930.f have rank \(0\).
Complex multiplication
The elliptic curves in class 6930.f do not have complex multiplication.Modular form 6930.2.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.
\(\left(\begin{array}{rrrr} 1 & 3 & 2 & 6 \\ 3 & 1 & 6 & 2 \\ 2 & 6 & 1 & 3 \\ 6 & 2 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
