Properties

Label 355740.bn
Number of curves $2$
Conductor $355740$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bn1")
 
E.isogeny_class()
 

Elliptic curves in class 355740.bn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
355740.bn1 355740bn2 \([0, -1, 0, -8592285060, -306515643083208]\) \(1314817350433665559504/190690249278375\) \(10174493597277089847878496000\) \([2]\) \(464486400\) \(4.3891\)  
355740.bn2 355740bn1 \([0, -1, 0, -488083185, -5697394525458]\) \(-3856034557002072064/1973796785296875\) \(-6582134780857465727262750000\) \([2]\) \(232243200\) \(4.0425\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 355740.bn have rank \(1\).

Complex multiplication

The elliptic curves in class 355740.bn do not have complex multiplication.

Modular form 355740.2.a.bn

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} + q^{9} - q^{15} - 2 q^{17} - 6 q^{19} + O(q^{20})\) 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 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.