Show commands:
SageMath
E = EllipticCurve("bm1")
E.isogeny_class()
Elliptic curves in class 386334bm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
386334.bm2 | 386334bm1 | \([1, -1, 1, -155059898, -736133011207]\) | \(117174888570509216929/1273887851544576\) | \(4482484929836171013390336\) | \([]\) | \(69543936\) | \(3.5453\) | \(\Gamma_0(N)\)-optimal |
386334.bm1 | 386334bm2 | \([1, -1, 1, -34011242258, 2414256301723673]\) | \(1236526859255318155975783969/38367061931916216\) | \(135003859800830791824728376\) | \([]\) | \(486807552\) | \(4.5183\) |
Rank
sage: E.rank()
The elliptic curves in class 386334bm have rank \(0\).
Complex multiplication
The elliptic curves in class 386334bm do not have complex multiplication.Modular form 386334.2.a.bm
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.