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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 309168.bd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
309168.bd1 | 309168bd1 | \([0, 0, 0, -12495, 513358]\) | \(1156019074000/58954473\) | \(11002319569152\) | \([2]\) | \(624640\) | \(1.2605\) | \(\Gamma_0(N)\)-optimal |
309168.bd2 | 309168bd2 | \([0, 0, 0, 7845, 2022586]\) | \(71527833500/2408785857\) | \(-1798149007107072\) | \([2]\) | \(1249280\) | \(1.6071\) |
Rank
sage: E.rank()
The elliptic curves in class 309168.bd have rank \(1\).
Complex multiplication
The elliptic curves in class 309168.bd do not have complex multiplication.Modular form 309168.2.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 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.