Properties

Label 303450bc
Number of curves $6$
Conductor $303450$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("303450.bc1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 303450bc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
303450.bc5 303450bc1 [1, 1, 0, -507513050, 4394954356500] [2] 141557760 \(\Gamma_0(N)\)-optimal
303450.bc4 303450bc2 [1, 1, 0, -655481050, 1623069812500] [2, 2] 283115520  
303450.bc6 303450bc3 [1, 1, 0, 2528142950, 12768937436500] [2] 566231040  
303450.bc2 303450bc4 [1, 1, 0, -6206593050, -186920449267500] [2, 2] 566231040  
303450.bc3 303450bc5 [1, 1, 0, -2114064050, -429734287366500] [2] 1132462080  
303450.bc1 303450bc6 [1, 1, 0, -99116914050, -12010780810048500] [2] 1132462080  

Rank

sage: E.rank()
 

The elliptic curves in class 303450bc have rank \(0\).

Modular form 303450.2.a.bc

sage: E.q_eigenform(10)
 
\( q - q^{2} - q^{3} + q^{4} + q^{6} + q^{7} - q^{8} + q^{9} - 4q^{11} - q^{12} + 2q^{13} - q^{14} + q^{16} - q^{18} + 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.