Properties

Label 2070b
Number of curves $2$
Conductor $2070$
CM no
Rank $0$
Graph

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

Elliptic curves in class 2070b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2070.f2 2070b1 \([1, -1, 0, 336, 44288]\) \(212776173/43335680\) \(-852976189440\) \([2]\) \(2688\) \(0.96856\) \(\Gamma_0(N)\)-optimal
2070.f1 2070b2 \([1, -1, 0, -16944, 828800]\) \(27333463470867/895491200\) \(17625953289600\) \([2]\) \(5376\) \(1.3151\)  

Rank

sage: E.rank()
 

The elliptic curves in class 2070b have rank \(0\).

Complex multiplication

The elliptic curves in class 2070b do not have complex multiplication.

Modular form 2070.2.a.b

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