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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 14490.bh
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
14490.bh1 | 14490bm1 | \([1, -1, 1, -1074488, -428409669]\) | \(188191720927962271801/9422571110400\) | \(6869054339481600\) | \([2]\) | \(221184\) | \(2.1097\) | \(\Gamma_0(N)\)-optimal |
14490.bh2 | 14490bm2 | \([1, -1, 1, -1016888, -476425029]\) | \(-159520003524722950201/42335913815758080\) | \(-30862881171687640320\) | \([2]\) | \(442368\) | \(2.4563\) |
Rank
sage: E.rank()
The elliptic curves in class 14490.bh have rank \(0\).
Complex multiplication
The elliptic curves in class 14490.bh do not have complex multiplication.Modular form 14490.2.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.