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Properties

Label 372810.cc
Number of curves $2$
Conductor $372810$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("cc1")
 
E.isogeny_class()
 

Elliptic curves in class 372810.cc

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 372810.cc have rank \(1\).

Complex multiplication

The elliptic curves in class 372810.cc do not have complex multiplication.

Modular form 372810.2.a.cc

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} + 4 q^{7} + q^{8} + q^{9} + q^{10} + 2 q^{11} - q^{12} - 6 q^{13} + 4 q^{14} - q^{15} + q^{16} + q^{18} - 2 q^{19} + O(q^{20})\) Copy content Toggle raw display

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.