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Properties

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

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Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 70602m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
70602.j2 70602m1 \([1, 0, 1, -4901065641, 132063422546476]\) \(1630513562870774583625/3950456832\) \(31544102424390219804672\) \([3]\) \(50585472\) \(3.9838\) \(\Gamma_0(N)\)-optimal
70602.j1 70602m2 \([1, 0, 1, -5059239336, 123084065637622]\) \(1793529535985843517625/218288998399868928\) \(1743021330562667002286768652288\) \([]\) \(151756416\) \(4.5331\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 70602.2.a.m

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.