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Properties

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

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Show commands: SageMath
E = EllipticCurve("t1")
 
E.isogeny_class()
 

Elliptic curves in class 24990.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
24990.t1 24990w4 \([1, 0, 1, -276370659, -1768445456354]\) \(19843180007106582309156121/1586964960000\) \(186704840579040000\) \([2]\) \(2949120\) \(3.2050\)  
24990.t2 24990w2 \([1, 0, 1, -17274339, -27629101538]\) \(4845512858070228485401/1370018429337600\) \(161181298193139302400\) \([2, 2]\) \(1474560\) \(2.8584\)  
24990.t3 24990w3 \([1, 0, 1, -15079139, -34909262818]\) \(-3223035316613162194201/2609328690805052160\) \(-306984911144523581571840\) \([2]\) \(2949120\) \(3.2050\)  
24990.t4 24990w1 \([1, 0, 1, -1218019, -314089954]\) \(1698623579042432281/620987846492160\) \(73058599151956131840\) \([2]\) \(737280\) \(2.5118\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 24990.2.a.t

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