Show commands:
SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 97104g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 97104.k4 | 97104g1 | \([0, -1, 0, -2119, -242942]\) | \(-2725888/64827\) | \(-25036258969008\) | \([2]\) | \(245760\) | \(1.2516\) | \(\Gamma_0(N)\)-optimal |
| 97104.k3 | 97104g2 | \([0, -1, 0, -72924, -7521696]\) | \(6940769488/35721\) | \(220727834175744\) | \([2, 2]\) | \(491520\) | \(1.5982\) | |
| 97104.k2 | 97104g3 | \([0, -1, 0, -113384, 1800288]\) | \(6522128932/3720087\) | \(91948909208067072\) | \([2]\) | \(983040\) | \(1.9448\) | |
| 97104.k1 | 97104g4 | \([0, -1, 0, -1165344, -483816816]\) | \(7080974546692/189\) | \(4671488553984\) | \([2]\) | \(983040\) | \(1.9448\) |
Rank
sage: E.rank()
The elliptic curves in class 97104g have rank \(0\).
Complex multiplication
The elliptic curves in class 97104g do not have complex multiplication.Modular form 97104.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
