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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 301665.bd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
301665.bd1 | 301665bd1 | \([0, 1, 1, -3729041, 2781915101]\) | \(-7030213029658624/33750556875\) | \(-27531366093795256875\) | \([3]\) | \(9345024\) | \(2.5793\) | \(\Gamma_0(N)\)-optimal |
301665.bd2 | 301665bd2 | \([0, 1, 1, 9189319, 14767246550]\) | \(105202686516002816/176321044921875\) | \(-143830493101594482421875\) | \([]\) | \(28035072\) | \(3.1286\) |
Rank
sage: E.rank()
The elliptic curves in class 301665.bd have rank \(1\).
Complex multiplication
The elliptic curves in class 301665.bd do not have complex multiplication.Modular form 301665.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.