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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 4140.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4140.g1 | 4140b2 | \([0, 0, 0, -90207, -10427994]\) | \(16110654114672/330625\) | \(1665969120000\) | \([2]\) | \(11520\) | \(1.4645\) | |
4140.g2 | 4140b1 | \([0, 0, 0, -5832, -151119]\) | \(69657034752/8984375\) | \(2829431250000\) | \([2]\) | \(5760\) | \(1.1179\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4140.g have rank \(1\).
Complex multiplication
The elliptic curves in class 4140.g do not have complex multiplication.Modular form 4140.2.a.g
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 LMFDB 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 LMFDB labels.