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SageMath
E = EllipticCurve("bm1")
E.isogeny_class()
Elliptic curves in class 338130.bm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 338130.bm1 | 338130bm2 | \([1, -1, 0, -460189629, -3799526720315]\) | \(3009261308803109129809313/85820312500000000\) | \(307372057382812500000000\) | \([2]\) | \(70778880\) | \(3.6082\) | |
| 338130.bm2 | 338130bm1 | \([1, -1, 0, -29929149, -54281346107]\) | \(827813553991775477153/123566310400000000\) | \(442562255303500800000000\) | \([2]\) | \(35389440\) | \(3.2616\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 338130.bm have rank \(1\).
Complex multiplication
The elliptic curves in class 338130.bm do not have complex multiplication.Modular form 338130.2.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 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.
