Properties

Label 249090t
Number of curves $2$
Conductor $249090$
CM no
Rank $1$
Graph

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

Elliptic curves in class 249090t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
249090.t2 249090t1 \([1, 1, 0, -88452, 10132176]\) \(-1626794704081/8125440\) \(-382268483312640\) \([2]\) \(1451520\) \(1.6456\) \(\Gamma_0(N)\)-optimal
249090.t1 249090t2 \([1, 1, 0, -1416932, 648599664]\) \(6687281588245201/165600\) \(7790797893600\) \([2]\) \(2903040\) \(1.9921\)  

Rank

sage: E.rank()
 

The elliptic curves in class 249090t have rank \(1\).

Complex multiplication

The elliptic curves in class 249090t do not have complex multiplication.

Modular form 249090.2.a.t

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