Properties

Label 24990e
Number of curves $4$
Conductor $24990$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 24990e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
24990.d3 24990e1 \([1, 1, 0, -881878, -319273772]\) \(-644706081631626841/347004000000\) \(-40824673596000000\) \([2]\) \(442368\) \(2.1365\) \(\Gamma_0(N)\)-optimal
24990.d2 24990e2 \([1, 1, 0, -14111878, -20410351772]\) \(2641739317048851306841/764694000\) \(89965484406000\) \([2]\) \(884736\) \(2.4831\)  
24990.d4 24990e3 \([1, 1, 0, 716747, -1295019347]\) \(346124368852751159/6361262220902400\) \(-748396139026946457600\) \([2]\) \(1327104\) \(2.6858\)  
24990.d1 24990e4 \([1, 1, 0, -14336053, -19728678227]\) \(2769646315294225853641/174474906948464640\) \(20526798327579916431360\) \([2]\) \(2654208\) \(3.0324\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 24990.2.a.e

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

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.