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SageMath
E = EllipticCurve("jg1")
E.isogeny_class()
Elliptic curves in class 382200.jg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
382200.jg1 | 382200jg3 | \([0, 1, 0, -2029008, 1107553488]\) | \(490757540836/2142075\) | \(4032207706800000000\) | \([2]\) | \(10616832\) | \(2.4230\) | |
382200.jg2 | 382200jg2 | \([0, 1, 0, -191508, -2296512]\) | \(1650587344/950625\) | \(447360322500000000\) | \([2, 2]\) | \(5308416\) | \(2.0764\) | |
382200.jg3 | 382200jg1 | \([0, 1, 0, -136383, -19385262]\) | \(9538484224/26325\) | \(774277481250000\) | \([2]\) | \(2654208\) | \(1.7298\) | \(\Gamma_0(N)\)-optimal |
382200.jg4 | 382200jg4 | \([0, 1, 0, 763992, -17584512]\) | \(26198797244/15234375\) | \(-28676943750000000000\) | \([2]\) | \(10616832\) | \(2.4230\) |
Rank
sage: E.rank()
The elliptic curves in class 382200.jg have rank \(1\).
Complex multiplication
The elliptic curves in class 382200.jg do not have complex multiplication.Modular form 382200.2.a.jg
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.