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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 177450.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
177450.c1 | 177450jp2 | \([1, 1, 0, -51275, -4449375]\) | \(434314041517/4592700\) | \(157658779687500\) | \([2]\) | \(884736\) | \(1.5405\) | |
177450.c2 | 177450jp1 | \([1, 1, 0, -5775, 55125]\) | \(620650477/317520\) | \(10899866250000\) | \([2]\) | \(442368\) | \(1.1939\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 177450.c have rank \(2\).
Complex multiplication
The elliptic curves in class 177450.c do not have complex multiplication.Modular form 177450.2.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.