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SageMath
E = EllipticCurve("bm1")
E.isogeny_class()
Elliptic curves in class 246225bm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
246225.bm2 | 246225bm1 | \([0, 1, 1, 292367, -9148856]\) | \(1503484706816/890163675\) | \(-1636357284376171875\) | \([]\) | \(4147200\) | \(2.1843\) | \(\Gamma_0(N)\)-optimal |
246225.bm1 | 246225bm2 | \([0, 1, 1, -3676633, 2995880269]\) | \(-2989967081734144/380653171875\) | \(-699741640905029296875\) | \([]\) | \(12441600\) | \(2.7336\) |
Rank
sage: E.rank()
The elliptic curves in class 246225bm have rank \(1\).
Complex multiplication
The elliptic curves in class 246225bm do not have complex multiplication.Modular form 246225.2.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.