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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 111012.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
111012.c1 | 111012a2 | \([0, -1, 0, -10372, -189848]\) | \(810448/363\) | \(55275741573888\) | \([2]\) | \(280896\) | \(1.3324\) | |
111012.c2 | 111012a1 | \([0, -1, 0, 2243, -23330]\) | \(131072/99\) | \(-942200140464\) | \([2]\) | \(140448\) | \(0.98578\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 111012.c have rank \(0\).
Complex multiplication
The elliptic curves in class 111012.c do not have complex multiplication.Modular form 111012.2.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.