↑

Properties

Label 24990.g
Number of curves $2$
Conductor $24990$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 24990.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
24990.g1 24990g2 \([1, 1, 0, -15558, 740328]\) \(3540302642521/849660\) \(99961649340\) \([2]\) \(49152\) \(1.0999\)  
24990.g2 24990g1 \([1, 1, 0, -858, 14148]\) \(-594823321/428400\) \(-50400831600\) \([2]\) \(24576\) \(0.75332\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 24990.g have rank \(1\).

Complex multiplication

The elliptic curves in class 24990.g do not have complex multiplication.

Modular form 24990.2.a.g

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} - q^{8} + q^{9} + q^{10} + 4 q^{11} - q^{12} - 4 q^{13} + q^{15} + q^{16} + q^{17} - q^{18} + 6 q^{19} + O(q^{20})\) 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.