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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 5776l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5776.m2 | 5776l1 | \([0, 1, 0, -89648, 10304852]\) | \(-413493625/152\) | \(-29290389143552\) | \([]\) | \(17280\) | \(1.5519\) | \(\Gamma_0(N)\)-optimal |
| 5776.m3 | 5776l2 | \([0, 1, 0, 54752, 39288820]\) | \(94196375/3511808\) | \(-676725150772625408\) | \([]\) | \(51840\) | \(2.1012\) | |
| 5776.m1 | 5776l3 | \([0, 1, 0, -493968, -1075051756]\) | \(-69173457625/2550136832\) | \(-491411185385426911232\) | \([]\) | \(155520\) | \(2.6505\) |
Rank
sage: E.rank()
The elliptic curves in class 5776l have rank \(1\).
Complex multiplication
The elliptic curves in class 5776l do not have complex multiplication.Modular form 5776.2.a.l
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.
