Show commands:
SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 19360m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 19360.c2 | 19360m1 | \([0, 1, 0, -504610, -138137100]\) | \(125330290485184/378125\) | \(42871776200000\) | \([2]\) | \(115200\) | \(1.8435\) | \(\Gamma_0(N)\)-optimal |
| 19360.c1 | 19360m2 | \([0, 1, 0, -511265, -134313137]\) | \(2036792051776/107421875\) | \(779486840000000000\) | \([2]\) | \(230400\) | \(2.1901\) |
Rank
sage: E.rank()
The elliptic curves in class 19360m have rank \(1\).
Complex multiplication
The elliptic curves in class 19360m do not have complex multiplication.Modular form 19360.2.a.m
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
