Properties

Label 361920a
Number of curves $2$
Conductor $361920$
CM no
Rank $3$
Graph

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 361920a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
361920.a1 361920a1 \([0, -1, 0, -2501, 48981]\) \(1690201440256/152685\) \(156349440\) \([2]\) \(368640\) \(0.61189\) \(\Gamma_0(N)\)-optimal
361920.a2 361920a2 \([0, -1, 0, -2321, 56145]\) \(-84433792336/31979025\) \(-523944345600\) \([2]\) \(737280\) \(0.95846\)  

Rank

sage: E.rank()
 

The elliptic curves in class 361920a have rank \(3\).

Complex multiplication

The elliptic curves in class 361920a do not have complex multiplication.

Modular form 361920.2.a.a

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