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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 200900e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
200900.e1 | 200900e1 | \([0, -1, 0, -54308, 5109112]\) | \(-768208/41\) | \(-945427364000000\) | \([]\) | \(870912\) | \(1.6325\) | \(\Gamma_0(N)\)-optimal |
200900.e2 | 200900e2 | \([0, -1, 0, 288692, 10597112]\) | \(115393712/68921\) | \(-1589263398884000000\) | \([]\) | \(2612736\) | \(2.1818\) |
Rank
sage: E.rank()
The elliptic curves in class 200900e have rank \(0\).
Complex multiplication
The elliptic curves in class 200900e do not have complex multiplication.Modular form 200900.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.