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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 324.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
324.c1 | 324a2 | \([0, 0, 0, -81, -243]\) | \(6912\) | \(8503056\) | \([]\) | \(54\) | \(0.054953\) | |
324.c2 | 324a1 | \([0, 0, 0, -21, 37]\) | \(790272\) | \(1296\) | \([3]\) | \(18\) | \(-0.49435\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 324.c have rank \(0\).
Complex multiplication
The elliptic curves in class 324.c do not have complex multiplication.Modular form 324.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.