Show commands:
SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 350168g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 350168.g1 | 350168g1 | \([0, 0, 0, -2853058, -1854872175]\) | \(33256413948450816/2481997\) | \(191682007321168\) | \([2]\) | \(5287680\) | \(2.1902\) | \(\Gamma_0(N)\)-optimal |
| 350168.g2 | 350168g2 | \([0, 0, 0, -2847143, -1862946150]\) | \(-2065624967846736/17960084863\) | \(-22192614209917994752\) | \([2]\) | \(10575360\) | \(2.5368\) |
Rank
sage: E.rank()
The elliptic curves in class 350168g have rank \(1\).
Complex multiplication
The elliptic curves in class 350168g do not have complex multiplication.Modular form 350168.2.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.
