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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 66924c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
66924.o2 | 66924c1 | \([0, 0, 0, -219024, -39447135]\) | \(764411904/143\) | \(217373914579536\) | \([2]\) | \(290304\) | \(1.7529\) | \(\Gamma_0(N)\)-optimal |
66924.o1 | 66924c2 | \([0, 0, 0, -241839, -30727242]\) | \(64314864/20449\) | \(497351516557978368\) | \([2]\) | \(580608\) | \(2.0995\) |
Rank
sage: E.rank()
The elliptic curves in class 66924c have rank \(0\).
Complex multiplication
The elliptic curves in class 66924c do not have complex multiplication.Modular form 66924.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.