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Properties

Label 24990b
Number of curves $2$
Conductor $24990$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 24990b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
24990.h2 24990b1 \([1, 1, 0, -35403, 2582973]\) \(-41713327443241/639221760\) \(-75203800842240\) \([2]\) \(120960\) \(1.4651\) \(\Gamma_0(N)\)-optimal
24990.h1 24990b2 \([1, 1, 0, -568523, 164758077]\) \(172735174415217961/39657600\) \(4665676982400\) \([2]\) \(241920\) \(1.8116\)  

Rank

sage: E.rank()
 

The elliptic curves in class 24990b have rank \(0\).

Complex multiplication

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

Modular form 24990.2.a.b

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