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SageMath
E = EllipticCurve("lf1")
E.isogeny_class()
Elliptic curves in class 369600lf
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
369600.lf2 | 369600lf1 | \([0, -1, 0, 25867, -4017363]\) | \(7476617216/31444875\) | \(-8049888000000000\) | \([]\) | \(1990656\) | \(1.7346\) | \(\Gamma_0(N)\)-optimal |
369600.lf1 | 369600lf2 | \([0, -1, 0, -238133, 122966637]\) | \(-5833703071744/22107421875\) | \(-5659500000000000000\) | \([]\) | \(5971968\) | \(2.2839\) |
Rank
sage: E.rank()
The elliptic curves in class 369600lf have rank \(0\).
Complex multiplication
The elliptic curves in class 369600lf do not have complex multiplication.Modular form 369600.2.a.lf
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.