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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 28611g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 28611.q1 | 28611g1 | \([0, 0, 1, -16626, -825431]\) | \(-2412468600832/970299\) | \(-204423563619\) | \([]\) | \(48384\) | \(1.1337\) | \(\Gamma_0(N)\)-optimal |
| 28611.q2 | 28611g2 | \([0, 0, 1, 10914, -3186986]\) | \(682417553408/21221529219\) | \(-4470972997388139\) | \([]\) | \(145152\) | \(1.6830\) |
Rank
sage: E.rank()
The elliptic curves in class 28611g have rank \(0\).
Complex multiplication
The elliptic curves in class 28611g do not have complex multiplication.Modular form 28611.2.a.g
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
