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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 2368c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2368.d3 | 2368c1 | \([0, -1, 0, -13, 23]\) | \(4096000/37\) | \(2368\) | \([]\) | \(96\) | \(-0.52996\) | \(\Gamma_0(N)\)-optimal |
2368.d2 | 2368c2 | \([0, -1, 0, -93, -305]\) | \(1404928000/50653\) | \(3241792\) | \([]\) | \(288\) | \(0.019349\) | |
2368.d1 | 2368c3 | \([0, -1, 0, -7493, -247169]\) | \(727057727488000/37\) | \(2368\) | \([]\) | \(864\) | \(0.56866\) |
Rank
sage: E.rank()
The elliptic curves in class 2368c have rank \(1\).
Complex multiplication
The elliptic curves in class 2368c do not have complex multiplication.Modular form 2368.2.a.c
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.