Properties

Label 353925bm
Number of curves $2$
Conductor $353925$
CM no
Rank $2$
Graph

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Show commands: SageMath
E = EllipticCurve("bm1")
 
E.isogeny_class()
 

Elliptic curves in class 353925bm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
353925.bm2 353925bm1 \([0, 0, 1, -3630, 78196]\) \(163840/13\) \(419727089925\) \([]\) \(388800\) \(0.97383\) \(\Gamma_0(N)\)-optimal
353925.bm1 353925bm2 \([0, 0, 1, -58080, -5372249]\) \(671088640/2197\) \(70933878197325\) \([]\) \(1166400\) \(1.5231\)  

Rank

sage: E.rank()
 

The elliptic curves in class 353925bm have rank \(2\).

Complex multiplication

The elliptic curves in class 353925bm do not have complex multiplication.

Modular form 353925.2.a.bm

sage: E.q_eigenform(10)
 
\(q - 2 q^{4} - 4 q^{7} + q^{13} + 4 q^{16} - 6 q^{17} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.