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SageMath
E = EllipticCurve("cc1")
E.isogeny_class()
Elliptic curves in class 204490.cc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
204490.cc1 | 204490u2 | \([1, 1, 1, -121467486, 515223359113]\) | \(-23178622194826561/1610510\) | \(-13771449395102102990\) | \([]\) | \(23040000\) | \(3.1265\) | |
204490.cc2 | 204490u1 | \([1, 1, 1, 204064, 143313633]\) | \(109902239/1100000\) | \(-9406085236733900000\) | \([]\) | \(4608000\) | \(2.3218\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 204490.cc have rank \(1\).
Complex multiplication
The elliptic curves in class 204490.cc do not have complex multiplication.Modular form 204490.2.a.cc
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.