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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 258570.bh
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
258570.bh1 | 258570bh2 | \([1, -1, 0, -230580, 41601600]\) | \(846509996114173/24354723600\) | \(39006841929166800\) | \([2]\) | \(3244032\) | \(1.9616\) | |
258570.bh2 | 258570bh1 | \([1, -1, 0, 3420, 2149200]\) | \(2761677827/1248480000\) | \(-1999581798240000\) | \([2]\) | \(1622016\) | \(1.6151\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 258570.bh have rank \(2\).
Complex multiplication
The elliptic curves in class 258570.bh do not have complex multiplication.Modular form 258570.2.a.bh
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.