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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 4950.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4950.u1 | 4950p2 | \([1, -1, 0, -207, 1381]\) | \(-53969305/10648\) | \(-194059800\) | \([]\) | \(2592\) | \(0.31338\) | |
4950.u2 | 4950p1 | \([1, -1, 0, 18, -14]\) | \(34295/22\) | \(-400950\) | \([]\) | \(864\) | \(-0.23592\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4950.u have rank \(1\).
Complex multiplication
The elliptic curves in class 4950.u do not have complex multiplication.Modular form 4950.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.