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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 37026p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
37026.s1 | 37026p1 | \([1, -1, 0, -2745, 35833]\) | \(1771561/612\) | \(790378397028\) | \([2]\) | \(92160\) | \(0.98473\) | \(\Gamma_0(N)\)-optimal |
37026.s2 | 37026p2 | \([1, -1, 0, 8145, 242743]\) | \(46268279/46818\) | \(-60463947372642\) | \([2]\) | \(184320\) | \(1.3313\) |
Rank
sage: E.rank()
The elliptic curves in class 37026p have rank \(1\).
Complex multiplication
The elliptic curves in class 37026p do not have complex multiplication.Modular form 37026.2.a.p
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.