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SageMath
E = EllipticCurve("ga1")
E.isogeny_class()
Elliptic curves in class 302400ga
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 302400.ga2 | 302400ga1 | \([0, 0, 0, -19500, 1342000]\) | \(-7414875/2744\) | \(-303464448000000\) | \([]\) | \(995328\) | \(1.4890\) | \(\Gamma_0(N)\)-optimal |
| 302400.ga1 | 302400ga2 | \([0, 0, 0, -1699500, 852766000]\) | \(-545407363875/14\) | \(-13934592000000\) | \([]\) | \(2985984\) | \(2.0383\) | |
| 302400.ga3 | 302400ga3 | \([0, 0, 0, 148500, -13554000]\) | \(4492125/3584\) | \(-288947699712000000\) | \([]\) | \(2985984\) | \(2.0383\) |
Rank
sage: E.rank()
The elliptic curves in class 302400ga have rank \(1\).
Complex multiplication
The elliptic curves in class 302400ga do not have complex multiplication.Modular form 302400.2.a.ga
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.
\(\left(\begin{array}{rrr} 1 & 3 & 3 \\ 3 & 1 & 9 \\ 3 & 9 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
