Properties

Label 350727.b
Number of curves $2$
Conductor $350727$
CM no
Rank $2$
Graph

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

Elliptic curves in class 350727.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
350727.b1 350727b2 \([1, 1, 1, -2104, -38014]\) \(84662348471/25857\) \(314602119\) \([2]\) \(211968\) \(0.60767\)  
350727.b2 350727b1 \([1, 1, 1, -149, -478]\) \(30080231/11271\) \(137134257\) \([2]\) \(105984\) \(0.26110\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 350727.b have rank \(2\).

Complex multiplication

The elliptic curves in class 350727.b do not have complex multiplication.

Modular form 350727.2.a.b

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} - q^{4} - 2 q^{5} + q^{6} + 3 q^{8} + q^{9} + 2 q^{10} - 2 q^{11} + q^{12} + q^{13} + 2 q^{15} - q^{16} + q^{17} - q^{18} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.