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SageMath
E = EllipticCurve("bm1")
E.isogeny_class()
Elliptic curves in class 426888.bm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
426888.bm1 | 426888bm2 | \([0, 0, 0, -174188091, 884738127350]\) | \(5476248398/891\) | \(95098497574575589484544\) | \([2]\) | \(68812800\) | \(3.4181\) | \(\Gamma_0(N)\)-optimal* |
426888.bm2 | 426888bm1 | \([0, 0, 0, -9836211, 16598626814]\) | \(-1972156/1089\) | \(-58115748517796193573888\) | \([2]\) | \(34406400\) | \(3.0716\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 426888.bm have rank \(1\).
Complex multiplication
The elliptic curves in class 426888.bm do not have complex multiplication.Modular form 426888.2.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.