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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 279312u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
279312.u2 | 279312u1 | \([0, -1, 0, -38, 63]\) | \(736000/297\) | \(2513808\) | \([]\) | \(41472\) | \(-0.073976\) | \(\Gamma_0(N)\)-optimal |
279312.u1 | 279312u2 | \([0, -1, 0, -1418, -20085]\) | \(37280608000/3993\) | \(33796752\) | \([]\) | \(124416\) | \(0.47533\) |
Rank
sage: E.rank()
The elliptic curves in class 279312u have rank \(1\).
Complex multiplication
The elliptic curves in class 279312u do not have complex multiplication.Modular form 279312.2.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 Cremona 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 Cremona labels.