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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 490049.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
490049.c1 | 490049c2 | \([1, -1, 0, -2644000, -1613913477]\) | \(17374804109361438921/482665506294457\) | \(56785114150036571593\) | \([2]\) | \(13436928\) | \(2.5699\) | \(\Gamma_0(N)\)-optimal* |
490049.c2 | 490049c1 | \([1, -1, 0, -2626115, -1637360712]\) | \(17024594875172176761/13702740137\) | \(1612113674377913\) | \([2]\) | \(6718464\) | \(2.2233\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 490049.c have rank \(1\).
Complex multiplication
The elliptic curves in class 490049.c do not have complex multiplication.Modular form 490049.2.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.