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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 3300g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3300.c1 | 3300g1 | \([0, -1, 0, -25333, -1270838]\) | \(57537462272/10673289\) | \(333540281250000\) | \([2]\) | \(11520\) | \(1.5049\) | \(\Gamma_0(N)\)-optimal |
| 3300.c2 | 3300g2 | \([0, -1, 0, 50292, -7472088]\) | \(28134667888/64304361\) | \(-32152180500000000\) | \([2]\) | \(23040\) | \(1.8515\) |
Rank
sage: E.rank()
The elliptic curves in class 3300g have rank \(0\).
Complex multiplication
The elliptic curves in class 3300g do not have complex multiplication.Modular form 3300.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
