Show commands:
SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 37026g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 37026.k2 | 37026g1 | \([1, -1, 0, -278262, 56546100]\) | \(1845026709625/793152\) | \(1024330402548288\) | \([2]\) | \(276480\) | \(1.8404\) | \(\Gamma_0(N)\)-optimal |
| 37026.k3 | 37026g2 | \([1, -1, 0, -234702, 74815164]\) | \(-1107111813625/1228691592\) | \(-1586815834847616648\) | \([2]\) | \(552960\) | \(2.1869\) | |
| 37026.k1 | 37026g3 | \([1, -1, 0, -817317, -214814187]\) | \(46753267515625/11591221248\) | \(14969690963384205312\) | \([2]\) | \(829440\) | \(2.3897\) | |
| 37026.k4 | 37026g4 | \([1, -1, 0, 1970523, -1363961835]\) | \(655215969476375/1001033261568\) | \(-1292802393218670715392\) | \([2]\) | \(1658880\) | \(2.7363\) |
Rank
sage: E.rank()
The elliptic curves in class 37026g have rank \(1\).
Complex multiplication
The elliptic curves in class 37026g do not have complex multiplication.Modular form 37026.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
