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SageMath
E = EllipticCurve("cc1")
E.isogeny_class()
Elliptic curves in class 446400cc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
446400.cc2 | 446400cc1 | \([0, 0, 0, -196524300, -1061931242000]\) | \(-281115640967896441/468084326400\) | \(-1397692309281177600000000\) | \([2]\) | \(76677120\) | \(3.5289\) | \(\Gamma_0(N)\)-optimal* |
446400.cc1 | 446400cc2 | \([0, 0, 0, -3145644300, -67906685162000]\) | \(1152829477932246539641/3188367360\) | \(9520413923082240000000\) | \([2]\) | \(153354240\) | \(3.8755\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 446400cc have rank \(1\).
Complex multiplication
The elliptic curves in class 446400cc do not have complex multiplication.Modular form 446400.2.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 Cremona 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 Cremona labels.