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SageMath
E = EllipticCurve("fu1")
E.isogeny_class()
Elliptic curves in class 123840.fu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
123840.fu1 | 123840ea2 | \([0, 0, 0, -5686092, 4776901776]\) | \(3940344055317123/369800000000\) | \(1908086774169600000000\) | \([2]\) | \(5308416\) | \(2.8217\) | |
123840.fu2 | 123840ea1 | \([0, 0, 0, -1262412, -462504816]\) | \(43121696645763/7045120000\) | \(36351271753482240000\) | \([2]\) | \(2654208\) | \(2.4751\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 123840.fu have rank \(1\).
Complex multiplication
The elliptic curves in class 123840.fu do not have complex multiplication.Modular form 123840.2.a.fu
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.