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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 7056bd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7056.by2 | 7056bd1 | \([0, 0, 0, 1029, 869162]\) | \(189/512\) | \(-326420926562304\) | \([]\) | \(24192\) | \(1.4639\) | \(\Gamma_0(N)\)-optimal |
7056.by1 | 7056bd2 | \([0, 0, 0, -657531, 205242282]\) | \(-67645179/8\) | \(-3718138366623744\) | \([]\) | \(72576\) | \(2.0132\) |
Rank
sage: E.rank()
The elliptic curves in class 7056bd have rank \(0\).
Complex multiplication
The elliptic curves in class 7056bd do not have complex multiplication.Modular form 7056.2.a.bd
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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.