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SageMath
E = EllipticCurve("bm1")
E.isogeny_class()
Elliptic curves in class 130536bm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
130536.h1 | 130536bm1 | \([0, 0, 0, -7444962, -7818830775]\) | \(33256413948450816/2481997\) | \(3405940080378192\) | \([2]\) | \(3760128\) | \(2.4300\) | \(\Gamma_0(N)\)-optimal |
130536.h2 | 130536bm2 | \([0, 0, 0, -7429527, -7852864950]\) | \(-2065624967846736/17960084863\) | \(-394333903751763564288\) | \([2]\) | \(7520256\) | \(2.7766\) |
Rank
sage: E.rank()
The elliptic curves in class 130536bm have rank \(1\).
Complex multiplication
The elliptic curves in class 130536bm do not have complex multiplication.Modular form 130536.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.