Show commands:
SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 362992.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
362992.g1 | 362992g2 | \([0, -1, 0, -25888, 819456]\) | \(3981876625/1714952\) | \(826418740625408\) | \([2]\) | \(1216512\) | \(1.5587\) | |
362992.g2 | 362992g1 | \([0, -1, 0, 5472, 91904]\) | \(37595375/29632\) | \(-14279373488128\) | \([2]\) | \(608256\) | \(1.2121\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 362992.g have rank \(0\).
Complex multiplication
The elliptic curves in class 362992.g do not have complex multiplication.Modular form 362992.2.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 LMFDB 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 LMFDB labels.