Show commands:
SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 4290m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4290.m2 | 4290m1 | \([1, 0, 1, -118, 1556]\) | \(-179501589721/955597500\) | \(-955597500\) | \([2]\) | \(2560\) | \(0.40731\) | \(\Gamma_0(N)\)-optimal |
4290.m1 | 4290m2 | \([1, 0, 1, -2868, 58756]\) | \(2607614922465721/5488604550\) | \(5488604550\) | \([2]\) | \(5120\) | \(0.75389\) |
Rank
sage: E.rank()
The elliptic curves in class 4290m have rank \(1\).
Complex multiplication
The elliptic curves in class 4290m do not have complex multiplication.Modular form 4290.2.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.