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Properties

Label 287490t
Number of curves $2$
Conductor $287490$
CM no
Rank $1$
Graph

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

Elliptic curves in class 287490t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
287490.t2 287490t1 \([1, 1, 0, 74547498, 7816558381524]\) \(352539190137707/203297472000000\) \(-26420893157060952145344000000\) \([2]\) \(414305280\) \(4.1327\) \(\Gamma_0(N)\)-optimal
287490.t1 287490t2 \([1, 1, 0, -5485125782, 152553756749076]\) \(140432610415556655253/3906984375000000\) \(507758486727181540921875000000\) \([2]\) \(828610560\) \(4.4793\)  

Rank

sage: E.rank()
 

The elliptic curves in class 287490t have rank \(1\).

Complex multiplication

The elliptic curves in class 287490t do not have complex multiplication.

Modular form 287490.2.a.t

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} - q^{7} - q^{8} + q^{9} - q^{10} + 6 q^{11} - q^{12} + 6 q^{13} + q^{14} - q^{15} + q^{16} + 6 q^{17} - q^{18} + 6 q^{19} + O(q^{20})\) 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.