Properties

Label 462400gm
Number of curves $2$
Conductor $462400$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("gm1")
 
E.isogeny_class()
 

Elliptic curves in class 462400gm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
462400.gm2 462400gm1 \([0, 1, 0, 337167, -19903537]\) \(27440/17\) \(-2626167507200000000\) \([]\) \(3317760\) \(2.2235\) \(\Gamma_0(N)\)-optimal
462400.gm1 462400gm2 \([0, 1, 0, -5442833, -5065843537]\) \(-115431760/4913\) \(-758962409580800000000\) \([]\) \(9953280\) \(2.7728\)  

Rank

sage: E.rank()
 

The elliptic curves in class 462400gm have rank \(0\).

Complex multiplication

The elliptic curves in class 462400gm do not have complex multiplication.

Modular form 462400.2.a.gm

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{7} - 2 q^{9} + q^{13} + 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.