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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 5568.bc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5568.bc1 | 5568bc2 | \([0, 1, 0, -416705, 103700031]\) | \(-30526075007211889/103499257854\) | \(-27131709450878976\) | \([]\) | \(37632\) | \(2.0174\) | |
5568.bc2 | 5568bc1 | \([0, 1, 0, -65, -70209]\) | \(-117649/8118144\) | \(-2128122740736\) | \([]\) | \(5376\) | \(1.0444\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 5568.bc have rank \(1\).
Complex multiplication
The elliptic curves in class 5568.bc do not have complex multiplication.Modular form 5568.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.