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SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 215600.bi
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
215600.bi1 | 215600s2 | \([0, 1, 0, -177008008, -906495216012]\) | \(237487154804983/151250\) | \(390622915760000000000\) | \([2]\) | \(28901376\) | \(3.2704\) | |
215600.bi2 | 215600s1 | \([0, 1, 0, -10996008, -14346728012]\) | \(-56933326423/1464100\) | \(-3781229824556800000000\) | \([2]\) | \(14450688\) | \(2.9238\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 215600.bi have rank \(0\).
Complex multiplication
The elliptic curves in class 215600.bi do not have complex multiplication.Modular form 215600.2.a.bi
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.