Properties

Label 24882.c
Number of curves $4$
Conductor $24882$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 24882.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
24882.c1 24882g4 \([1, 1, 0, -1150101, 474257025]\) \(168241156610234677286617/17467164\) \(17467164\) \([2]\) \(159744\) \(1.7349\)  
24882.c2 24882g2 \([1, 1, 0, -71881, 7387765]\) \(41074802461509814297/418521012624\) \(418521012624\) \([2, 2]\) \(79872\) \(1.3883\)  
24882.c3 24882g3 \([1, 1, 0, -70141, 7764649]\) \(-38163592211939879257/4156203493184028\) \(-4156203493184028\) \([2]\) \(159744\) \(1.7349\)  
24882.c4 24882g1 \([1, 1, 0, -4601, 108069]\) \(10775263270478617/1009793571072\) \(1009793571072\) \([2]\) \(39936\) \(1.0418\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 24882.c have rank \(1\).

Complex multiplication

The elliptic curves in class 24882.c do not have complex multiplication.

Modular form 24882.2.a.c

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

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.