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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 369600.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
369600.c1 | 369600c2 | \([0, -1, 0, -20273, -631983]\) | \(449955166736/174330387\) | \(357028632576000\) | \([2]\) | \(1720320\) | \(1.4913\) | |
369600.c2 | 369600c1 | \([0, -1, 0, 4027, -73083]\) | \(56409309184/50014503\) | \(-6401856384000\) | \([2]\) | \(860160\) | \(1.1447\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 369600.c have rank \(0\).
Complex multiplication
The elliptic curves in class 369600.c do not have complex multiplication.Modular form 369600.2.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.