Properties

Label 740.b
Number of curves $2$
Conductor $740$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 740.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
740.b1 740b2 \([0, 1, 0, -12021, -511321]\) \(750484394082304/578125\) \(148000000\) \([]\) \(432\) \(0.87559\)  
740.b2 740b1 \([0, 1, 0, -181, -425]\) \(2575826944/1266325\) \(324179200\) \([3]\) \(144\) \(0.32628\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 740.b have rank \(1\).

Complex multiplication

The elliptic curves in class 740.b do not have complex multiplication.

Modular form 740.2.a.b

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} - q^{7} - 2 q^{9} - 3 q^{11} - 4 q^{13} - q^{15} - 4 q^{19} + O(q^{20})\) 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 LMFDB 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 LMFDB labels.