Show commands:
SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 302016z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 302016.z3 | 302016z1 | \([0, -1, 0, -3549, -45747]\) | \(2725888/1053\) | \(1910224622592\) | \([2]\) | \(368640\) | \(1.0555\) | \(\Gamma_0(N)\)-optimal |
| 302016.z2 | 302016z2 | \([0, -1, 0, -25329, 1526769]\) | \(61918288/1521\) | \(44147413499904\) | \([2, 2]\) | \(737280\) | \(1.4021\) | |
| 302016.z1 | 302016z3 | \([0, -1, 0, -402849, 98549409]\) | \(62275269892/39\) | \(4527939846144\) | \([2]\) | \(1474560\) | \(1.7486\) | |
| 302016.z4 | 302016z4 | \([0, -1, 0, 3711, 4796673]\) | \(48668/85683\) | \(-9947883841978368\) | \([2]\) | \(1474560\) | \(1.7486\) |
Rank
sage: E.rank()
The elliptic curves in class 302016z have rank \(1\).
Complex multiplication
The elliptic curves in class 302016z do not have complex multiplication.Modular form 302016.2.a.z
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.
