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Properties

Label 38829c
Number of curves $2$
Conductor $38829$
CM no
Rank $2$
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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 38829c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
38829.g2 38829c1 \([1, 1, 0, 5, 64]\) \(125/21\) \(-1669647\) \([2]\) \(6336\) \(-0.12671\) \(\Gamma_0(N)\)-optimal
38829.g1 38829c2 \([1, 1, 0, -210, 1053]\) \(12977875/441\) \(35062587\) \([2]\) \(12672\) \(0.21986\)  

Rank

sage: E.rank()
 

The elliptic curves in class 38829c have rank \(2\).

Complex multiplication

The elliptic curves in class 38829c do not have complex multiplication.

Modular form 38829.2.a.c

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} - q^{4} - q^{6} + q^{7} - 3 q^{8} + q^{9} + 2 q^{11} + q^{12} - 6 q^{13} + q^{14} - q^{16} - 6 q^{17} + q^{18} + 4 q^{19} + O(q^{20})\) 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 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.