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SageMath
E = EllipticCurve("bt1")
E.isogeny_class()
Elliptic curves in class 37440bt
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
37440.q2 | 37440bt1 | \([0, 0, 0, -963, 11988]\) | \(-2116874304/105625\) | \(-4928040000\) | \([2]\) | \(16384\) | \(0.62092\) | \(\Gamma_0(N)\)-optimal |
37440.q1 | 37440bt2 | \([0, 0, 0, -15588, 749088]\) | \(140283769536/325\) | \(970444800\) | \([2]\) | \(32768\) | \(0.96749\) |
Rank
sage: E.rank()
The elliptic curves in class 37440bt have rank \(1\).
Complex multiplication
The elliptic curves in class 37440bt do not have complex multiplication.Modular form 37440.2.a.bt
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.