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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 62866e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
62866.e2 | 62866e1 | \([1, -1, 1, -203737, 36268857]\) | \(-80017281/2176\) | \(-25433523804059776\) | \([]\) | \(455112\) | \(1.9294\) | \(\Gamma_0(N)\)-optimal |
62866.e1 | 62866e2 | \([1, -1, 1, -2588947, -4976806507]\) | \(-164189503521/820677346\) | \(-9592241183338051926946\) | \([]\) | \(3185784\) | \(2.9023\) |
Rank
sage: E.rank()
The elliptic curves in class 62866e have rank \(0\).
Complex multiplication
The elliptic curves in class 62866e do not have complex multiplication.Modular form 62866.2.a.e
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.