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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 369600.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
369600.u1 | 369600u2 | \([0, -1, 0, -1793, -22143]\) | \(77860436/17787\) | \(145711104000\) | \([2]\) | \(294912\) | \(0.85456\) | |
369600.u2 | 369600u1 | \([0, -1, 0, -593, 5457]\) | \(11279504/693\) | \(1419264000\) | \([2]\) | \(147456\) | \(0.50799\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 369600.u have rank \(2\).
Complex multiplication
The elliptic curves in class 369600.u do not have complex multiplication.Modular form 369600.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.