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Properties

Label 70602v
Number of curves $2$
Conductor $70602$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("v1")
 
E.isogeny_class()
 

Elliptic curves in class 70602v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
70602.p2 70602v1 \([1, 1, 1, 211, -673]\) \(15069223/12348\) \(-851036508\) \([2]\) \(34560\) \(0.40128\) \(\Gamma_0(N)\)-optimal
70602.p1 70602v2 \([1, 1, 1, -1019, -7069]\) \(1697936057/705894\) \(48650920374\) \([2]\) \(69120\) \(0.74786\)  

Rank

sage: E.rank()
 

The elliptic curves in class 70602v have rank \(1\).

Complex multiplication

The elliptic curves in class 70602v do not have complex multiplication.

Modular form 70602.2.a.v

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - 2 q^{5} - q^{6} + q^{7} + q^{8} + q^{9} - 2 q^{10} + 4 q^{11} - q^{12} - 2 q^{13} + q^{14} + 2 q^{15} + q^{16} + 2 q^{17} + q^{18} - 8 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.