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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 38514.bd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
38514.bd1 | 38514bh1 | \([1, 0, 0, -3480, 78336]\) | \(39616946929/226368\) | \(26631968832\) | \([2]\) | \(82944\) | \(0.84192\) | \(\Gamma_0(N)\)-optimal |
38514.bd2 | 38514bh2 | \([1, 0, 0, -1520, 166536]\) | \(-3301293169/100082952\) | \(-11774659219848\) | \([2]\) | \(165888\) | \(1.1885\) |
Rank
sage: E.rank()
The elliptic curves in class 38514.bd have rank \(1\).
Complex multiplication
The elliptic curves in class 38514.bd do not have complex multiplication.Modular form 38514.2.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.