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SageMath
E = EllipticCurve("cc1")
E.isogeny_class()
Elliptic curves in class 372810cc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
372810.cc1 | 372810cc1 | \([1, 1, 1, -55205, 4580075]\) | \(770842973809/66873600\) | \(1614166134278400\) | \([2]\) | \(3153920\) | \(1.6589\) | \(\Gamma_0(N)\)-optimal |
372810.cc2 | 372810cc2 | \([1, 1, 1, 60395, 21365195]\) | \(1009328859791/8734528080\) | \(-210830274213437520\) | \([2]\) | \(6307840\) | \(2.0055\) |
Rank
sage: E.rank()
The elliptic curves in class 372810cc have rank \(1\).
Complex multiplication
The elliptic curves in class 372810cc do not have complex multiplication.Modular form 372810.2.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.