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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 2205g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2205.e2 | 2205g1 | \([0, 0, 1, -588, 6088]\) | \(-262144/35\) | \(-3001814235\) | \([]\) | \(960\) | \(0.55111\) | \(\Gamma_0(N)\)-optimal |
| 2205.e3 | 2205g2 | \([0, 0, 1, 3822, -15521]\) | \(71991296/42875\) | \(-3677222437875\) | \([]\) | \(2880\) | \(1.1004\) | |
| 2205.e1 | 2205g3 | \([0, 0, 1, -57918, -5612252]\) | \(-250523582464/13671875\) | \(-1172583685546875\) | \([]\) | \(8640\) | \(1.6497\) |
Rank
sage: E.rank()
The elliptic curves in class 2205g have rank \(1\).
Complex multiplication
The elliptic curves in class 2205g do not have complex multiplication.Modular form 2205.2.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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
