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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 322.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
322.c1 | 322d2 | \([1, 0, 0, -174, 868]\) | \(582810602977/829472\) | \(829472\) | \([2]\) | \(80\) | \(0.038652\) | |
322.c2 | 322d1 | \([1, 0, 0, -14, 4]\) | \(304821217/164864\) | \(164864\) | \([2]\) | \(40\) | \(-0.30792\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 322.c have rank \(1\).
Complex multiplication
The elliptic curves in class 322.c do not have complex multiplication.Modular form 322.2.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 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.