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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 379050p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
379050.p1 | 379050p1 | \([1, 1, 0, -11788500, 14202450000]\) | \(1690513270434786979/164670952320000\) | \(17648094718170000000000\) | \([2]\) | \(38707200\) | \(3.0059\) | \(\Gamma_0(N)\)-optimal |
379050.p2 | 379050p2 | \([1, 1, 0, 14279500, 68241414000]\) | \(3004566620369762141/20506979587500000\) | \(-2197771452979101562500000\) | \([2]\) | \(77414400\) | \(3.3525\) |
Rank
sage: E.rank()
The elliptic curves in class 379050p have rank \(1\).
Complex multiplication
The elliptic curves in class 379050p do not have complex multiplication.Modular form 379050.2.a.p
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.