Properties

Label 291312be
Number of curves $4$
Conductor $291312$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("be1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 291312be

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
291312.be4 291312be1 \([0, 0, 0, 40749, 855500690]\) \(103823/4386816\) \(-316177108443265499136\) \([2]\) \(10616832\) \(2.6125\) \(\Gamma_0(N)\)-optimal
291312.be3 291312be2 \([0, 0, 0, -13276371, 18287610770]\) \(3590714269297/73410624\) \(5291026299105271087104\) \([2, 2]\) \(21233664\) \(2.9590\)  
291312.be1 291312be3 \([0, 0, 0, -211368531, 1182792182546]\) \(14489843500598257/6246072\) \(450181859482696384512\) \([2]\) \(42467328\) \(3.3056\)  
291312.be2 291312be4 \([0, 0, 0, -28258131, -30561915886]\) \(34623662831857/14438442312\) \(1040641991967079775895552\) \([2]\) \(42467328\) \(3.3056\)  

Rank

sage: E.rank()
 

The elliptic curves in class 291312be have rank \(1\).

Complex multiplication

The elliptic curves in class 291312be do not have complex multiplication.

Modular form 291312.2.a.be

sage: E.q_eigenform(10)
 
\(q - 2q^{5} - q^{7} - 6q^{13} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.