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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 51376.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
51376.u1 | 51376o2 | \([0, 1, 0, -189336, 35039252]\) | \(-37966934881/4952198\) | \(-97907973636841472\) | \([]\) | \(561600\) | \(1.9934\) | |
51376.u2 | 51376o1 | \([0, 1, 0, -56, -166828]\) | \(-1/608\) | \(-12020530675712\) | \([]\) | \(112320\) | \(1.1887\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 51376.u have rank \(0\).
Complex multiplication
The elliptic curves in class 51376.u do not have complex multiplication.Modular form 51376.2.a.u
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.