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SageMath
E = EllipticCurve("bm1")
E.isogeny_class()
Elliptic curves in class 115600bm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
115600.bf2 | 115600bm1 | \([0, -1, 0, 3372, 18892]\) | \(27440/17\) | \(-2626167507200\) | \([]\) | \(82944\) | \(1.0722\) | \(\Gamma_0(N)\)-optimal |
115600.bf1 | 115600bm2 | \([0, -1, 0, -54428, 5082172]\) | \(-115431760/4913\) | \(-758962409580800\) | \([]\) | \(248832\) | \(1.6215\) |
Rank
sage: E.rank()
The elliptic curves in class 115600bm have rank \(0\).
Complex multiplication
The elliptic curves in class 115600bm do not have complex multiplication.Modular form 115600.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.