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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 5776q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5776.c3 | 5776q1 | \([0, 1, 0, 3851, -2781]\) | \(32768/19\) | \(-3661298642944\) | \([]\) | \(8640\) | \(1.1002\) | \(\Gamma_0(N)\)-optimal |
5776.c2 | 5776q2 | \([0, 1, 0, -53909, -5143421]\) | \(-89915392/6859\) | \(-1321728810102784\) | \([]\) | \(25920\) | \(1.6495\) | |
5776.c1 | 5776q3 | \([0, 1, 0, -4443669, -3606941501]\) | \(-50357871050752/19\) | \(-3661298642944\) | \([]\) | \(77760\) | \(2.1988\) |
Rank
sage: E.rank()
The elliptic curves in class 5776q have rank \(1\).
Complex multiplication
The elliptic curves in class 5776q do not have complex multiplication.Modular form 5776.2.a.q
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 Cremona numbering.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.