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SageMath
E = EllipticCurve("jf1")
E.isogeny_class()
Elliptic curves in class 277200jf
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
277200.jf1 | 277200jf1 | \([0, 0, 0, -27075, 1687250]\) | \(188183524/3465\) | \(40415760000000\) | \([2]\) | \(884736\) | \(1.4055\) | \(\Gamma_0(N)\)-optimal |
277200.jf2 | 277200jf2 | \([0, 0, 0, -75, 4900250]\) | \(-2/444675\) | \(-10373378400000000\) | \([2]\) | \(1769472\) | \(1.7521\) |
Rank
sage: E.rank()
The elliptic curves in class 277200jf have rank \(1\).
Complex multiplication
The elliptic curves in class 277200jf do not have complex multiplication.Modular form 277200.2.a.jf
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.