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SageMath
E = EllipticCurve("et1")
E.isogeny_class()
Elliptic curves in class 316050et
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
316050.et2 | 316050et1 | \([1, 0, 1, 194749, -73889602]\) | \(444369620591/1540767744\) | \(-2832340379904000000\) | \([]\) | \(8890560\) | \(2.2236\) | \(\Gamma_0(N)\)-optimal |
316050.et1 | 316050et2 | \([1, 0, 1, -73378751, 241960287398]\) | \(-23769846831649063249/3261823333284\) | \(-5996097708398895562500\) | \([]\) | \(62233920\) | \(3.1966\) |
Rank
sage: E.rank()
The elliptic curves in class 316050et have rank \(1\).
Complex multiplication
The elliptic curves in class 316050et do not have complex multiplication.Modular form 316050.2.a.et
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.