Show commands:
SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 40362.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
40362.m1 | 40362n2 | \([1, 0, 1, -110305042, -38151639004]\) | \(167239798814188068697/96074132133998592\) | \(85266145917804135648817152\) | \([2]\) | \(11059200\) | \(3.6653\) | |
40362.m2 | 40362n1 | \([1, 0, 1, 27463918, -4756443100]\) | \(2581315285024874663/1504839620100096\) | \(-1335550702153476788453376\) | \([2]\) | \(5529600\) | \(3.3187\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 40362.m have rank \(1\).
Complex multiplication
The elliptic curves in class 40362.m do not have complex multiplication.Modular form 40362.2.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 LMFDB 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 LMFDB labels.