Show commands:
SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 966.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
966.f1 | 966f4 | \([1, 0, 1, -1516491, -715440266]\) | \(385693937170561837203625/2159357734550274048\) | \(2159357734550274048\) | \([2]\) | \(28800\) | \(2.3604\) | |
966.f2 | 966f2 | \([1, 0, 1, -111996, 13735450]\) | \(155355156733986861625/8291568305839392\) | \(8291568305839392\) | \([6]\) | \(9600\) | \(1.8111\) | |
966.f3 | 966f3 | \([1, 0, 1, -41931, -23576714]\) | \(-8152944444844179625/235342826399858688\) | \(-235342826399858688\) | \([2]\) | \(14400\) | \(2.0138\) | |
966.f4 | 966f1 | \([1, 0, 1, 4644, 858394]\) | \(11079872671250375/324440155855872\) | \(-324440155855872\) | \([6]\) | \(4800\) | \(1.4645\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 966.f have rank \(0\).
Complex multiplication
The elliptic curves in class 966.f do not have complex multiplication.Modular form 966.2.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.