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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 30400g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 30400.k3 | 30400g1 | \([0, 1, 0, 67, 13]\) | \(32768/19\) | \(-19000000\) | \([]\) | \(5184\) | \(0.086119\) | \(\Gamma_0(N)\)-optimal |
| 30400.k2 | 30400g2 | \([0, 1, 0, -933, -11987]\) | \(-89915392/6859\) | \(-6859000000\) | \([]\) | \(15552\) | \(0.63543\) | |
| 30400.k1 | 30400g3 | \([0, 1, 0, -76933, -8238987]\) | \(-50357871050752/19\) | \(-19000000\) | \([]\) | \(46656\) | \(1.1847\) |
Rank
sage: E.rank()
The elliptic curves in class 30400g have rank \(1\).
Complex multiplication
The elliptic curves in class 30400g do not have complex multiplication.Modular form 30400.2.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.
