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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 16900.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
16900.e1 | 16900h2 | \([0, -1, 0, -7258, -232363]\) | \(1000939264/15625\) | \(660156250000\) | \([]\) | \(20736\) | \(1.0689\) | |
16900.e2 | 16900h1 | \([0, -1, 0, -758, 8137]\) | \(1141504/25\) | \(1056250000\) | \([]\) | \(6912\) | \(0.51961\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 16900.e have rank \(2\).
Complex multiplication
The elliptic curves in class 16900.e do not have complex multiplication.Modular form 16900.2.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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.