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Properties

Label 70602br
Number of curves $2$
Conductor $70602$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("br1")
 
E.isogeny_class()
 

Elliptic curves in class 70602br

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
70602.bb2 70602br1 \([1, 0, 0, -806915, -290832099]\) \(-12232183057921/610094268\) \(-2898011369836590588\) \([2]\) \(3225600\) \(2.3036\) \(\Gamma_0(N)\)-optimal
70602.bb1 70602br2 \([1, 0, 0, -13061405, -18170133009]\) \(51878840608939681/120094002\) \(570459028218862482\) \([2]\) \(6451200\) \(2.6502\)  

Rank

sage: E.rank()
 

The elliptic curves in class 70602br have rank \(0\).

Complex multiplication

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

Modular form 70602.2.a.br

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