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SageMath
E = EllipticCurve("ek1")
E.isogeny_class()
Elliptic curves in class 46800ek
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
46800.p1 | 46800ek1 | \([0, 0, 0, -3675, 18250]\) | \(117649/65\) | \(3032640000000\) | \([2]\) | \(73728\) | \(1.0856\) | \(\Gamma_0(N)\)-optimal |
46800.p2 | 46800ek2 | \([0, 0, 0, 14325, 144250]\) | \(6967871/4225\) | \(-197121600000000\) | \([2]\) | \(147456\) | \(1.4321\) |
Rank
sage: E.rank()
The elliptic curves in class 46800ek have rank \(0\).
Complex multiplication
The elliptic curves in class 46800ek do not have complex multiplication.Modular form 46800.2.a.ek
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.