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Properties

Label 64974.i
Number of curves $2$
Conductor $64974$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 64974.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
64974.i1 64974l1 \([1, 1, 0, -9670665, 11536465221]\) \(850167619482740847625/2955180493504512\) \(347674029880312332288\) \([2]\) \(5160960\) \(2.8043\) \(\Gamma_0(N)\)-optimal
64974.i2 64974l2 \([1, 1, 0, -5405705, 21774928197]\) \(-148488432493486191625/1655470281336947712\) \(-194764423129010561369088\) \([2]\) \(10321920\) \(3.1508\)  

Rank

sage: E.rank()
 

The elliptic curves in class 64974.i have rank \(1\).

Complex multiplication

The elliptic curves in class 64974.i do not have complex multiplication.

Modular form 64974.2.a.i

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