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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 14490.bc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
14490.bc1 | 14490w1 | \([1, -1, 0, -1010574, -390768620]\) | \(156567200830221067489/16905000000\) | \(12323745000000\) | \([2]\) | \(139776\) | \(1.9387\) | \(\Gamma_0(N)\)-optimal |
14490.bc2 | 14490w2 | \([1, -1, 0, -1008054, -392816372]\) | \(-155398856216042825569/1627294921875000\) | \(-1186297998046875000\) | \([2]\) | \(279552\) | \(2.2853\) |
Rank
sage: E.rank()
The elliptic curves in class 14490.bc have rank \(0\).
Complex multiplication
The elliptic curves in class 14490.bc do not have complex multiplication.Modular form 14490.2.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.