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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 417450.bc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
417450.bc1 | 417450bc2 | \([1, 1, 0, -84858875, -298694115375]\) | \(1834261866512531/15618460500\) | \(575429888639839148437500\) | \([2]\) | \(66908160\) | \(3.3841\) | \(\Gamma_0(N)\)-optimal* |
417450.bc2 | 417450bc1 | \([1, 1, 0, -1671375, -10948552875]\) | \(-14014952531/1397250000\) | \(-51478787675777343750000\) | \([2]\) | \(33454080\) | \(3.0375\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 417450.bc have rank \(0\).
Complex multiplication
The elliptic curves in class 417450.bc do not have complex multiplication.Modular form 417450.2.a.bc
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.