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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 6630x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6630.ba1 | 6630x1 | \([1, 0, 0, -657450, 205128612]\) | \(31427652507069423952801/654426190080\) | \(654426190080\) | \([2]\) | \(48640\) | \(1.7966\) | \(\Gamma_0(N)\)-optimal |
6630.ba2 | 6630x2 | \([1, 0, 0, -656730, 205600500]\) | \(-31324512477868037557921/143427974919699600\) | \(-143427974919699600\) | \([2]\) | \(97280\) | \(2.1432\) |
Rank
sage: E.rank()
The elliptic curves in class 6630x have rank \(0\).
Complex multiplication
The elliptic curves in class 6630x do not have complex multiplication.Modular form 6630.2.a.x
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.