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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 882.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
882.c1 | 882c2 | \([1, -1, 0, -62190, 6208852]\) | \(-6329617441/279936\) | \(-1176442217564544\) | \([]\) | \(4704\) | \(1.6567\) | |
882.c2 | 882c1 | \([1, -1, 0, -450, -8366]\) | \(-2401/6\) | \(-25215239574\) | \([]\) | \(672\) | \(0.68378\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 882.c have rank \(0\).
Complex multiplication
The elliptic curves in class 882.c do not have complex multiplication.Modular form 882.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.