Show commands:
SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 124215.t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 124215.t1 | 124215be4 | \([1, 1, 1, -931785, 345782562]\) | \(157551496201/13125\) | \(7453283933038125\) | \([2]\) | \(1474560\) | \(2.0895\) | |
| 124215.t2 | 124215be2 | \([1, 1, 1, -62280, 4588800]\) | \(47045881/11025\) | \(6260758503752025\) | \([2, 2]\) | \(737280\) | \(1.7429\) | |
| 124215.t3 | 124215be1 | \([1, 1, 1, -20875, -1108528]\) | \(1771561/105\) | \(59626271464305\) | \([2]\) | \(368640\) | \(1.3963\) | \(\Gamma_0(N)\)-optimal |
| 124215.t4 | 124215be3 | \([1, 1, 1, 144745, 28852130]\) | \(590589719/972405\) | \(-552198900030928605\) | \([2]\) | \(1474560\) | \(2.0895\) |
Rank
sage: E.rank()
The elliptic curves in class 124215.t have rank \(1\).
Complex multiplication
The elliptic curves in class 124215.t do not have complex multiplication.Modular form 124215.2.a.t
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
