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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 130.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
130.c1 | 130c1 | \([1, 1, 1, -841, -9737]\) | \(65787589563409/10400000\) | \(10400000\) | \([2]\) | \(80\) | \(0.35695\) | \(\Gamma_0(N)\)-optimal |
130.c2 | 130c2 | \([1, 1, 1, -761, -11561]\) | \(-48743122863889/26406250000\) | \(-26406250000\) | \([2]\) | \(160\) | \(0.70352\) |
Rank
sage: E.rank()
The elliptic curves in class 130.c have rank \(0\).
Complex multiplication
The elliptic curves in class 130.c do not have complex multiplication.Modular form 130.2.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.