Properties

Label 355740bv
Number of curves $4$
Conductor $355740$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bv1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 355740bv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
355740.bv4 355740bv1 \([0, -1, 0, 1296475, -2088123750]\) \(72268906496/606436875\) \(-2022320269779766110000\) \([2]\) \(12441600\) \(2.7696\) \(\Gamma_0(N)\)-optimal
355740.bv3 355740bv2 \([0, -1, 0, -18713900, -28685914200]\) \(13584145739344/1195803675\) \(63803455504044294931200\) \([2]\) \(24883200\) \(3.1161\)  
355740.bv2 355740bv3 \([0, -1, 0, -92618885, -343322540658]\) \(-26348629355659264/24169921875\) \(-80600842300042968750000\) \([2]\) \(37324800\) \(3.3189\)  
355740.bv1 355740bv4 \([0, -1, 0, -1482228260, -21963976884408]\) \(6749703004355978704/5671875\) \(302629295889228000000\) \([2]\) \(74649600\) \(3.6655\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 355740.2.a.bv

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} + q^{9} + 2q^{13} - q^{15} + 2q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.