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SageMath
E = EllipticCurve("fe1")
E.isogeny_class()
Elliptic curves in class 115920.fe
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
115920.fe1 | 115920cr2 | \([0, 0, 0, -3613707, -2644097094]\) | \(64733826967442667/20736800\) | \(1671833331302400\) | \([2]\) | \(1843200\) | \(2.2816\) | |
115920.fe2 | 115920cr1 | \([0, 0, 0, -226827, -40941126]\) | \(16008724040427/282741760\) | \(22795084030279680\) | \([2]\) | \(921600\) | \(1.9350\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 115920.fe have rank \(1\).
Complex multiplication
The elliptic curves in class 115920.fe do not have complex multiplication.Modular form 115920.2.a.fe
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.