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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 13650p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
13650.i2 | 13650p1 | \([1, 1, 0, -695, -7275]\) | \(297676210733/3634176\) | \(454272000\) | \([2]\) | \(7680\) | \(0.47170\) | \(\Gamma_0(N)\)-optimal |
13650.i1 | 13650p2 | \([1, 1, 0, -11095, -454475]\) | \(1208528172090413/183456\) | \(22932000\) | \([2]\) | \(15360\) | \(0.81827\) |
Rank
sage: E.rank()
The elliptic curves in class 13650p have rank \(1\).
Complex multiplication
The elliptic curves in class 13650p do not have complex multiplication.Modular form 13650.2.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.