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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 119350f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
119350.s2 | 119350f1 | \([1, 0, 1, -12876, 725898]\) | \(-15107691357361/5868735488\) | \(-91698992000000\) | \([]\) | \(320000\) | \(1.3884\) | \(\Gamma_0(N)\)-optimal |
119350.s1 | 119350f2 | \([1, 0, 1, -93376, -69218102]\) | \(-5762391987245041/129101095135628\) | \(-2017204611494187500\) | \([]\) | \(1600000\) | \(2.1931\) |
Rank
sage: E.rank()
The elliptic curves in class 119350f have rank \(1\).
Complex multiplication
The elliptic curves in class 119350f do not have complex multiplication.Modular form 119350.2.a.f
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.