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Properties

Label 182070ec
Number of curves $2$
Conductor $182070$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("ec1")
 
E.isogeny_class()
 

Elliptic curves in class 182070ec

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
182070.b2 182070ec1 \([1, -1, 0, 21315, 865925]\) \(11074654989/9800000\) \(-947685274200000\) \([2]\) \(1013760\) \(1.5612\) \(\Gamma_0(N)\)-optimal
182070.b1 182070ec2 \([1, -1, 0, -107205, 7780301]\) \(1409071586931/546875000\) \(52884222890625000\) \([2]\) \(2027520\) \(1.9078\)  

Rank

sage: E.rank()
 

The elliptic curves in class 182070ec have rank \(1\).

Complex multiplication

The elliptic curves in class 182070ec do not have complex multiplication.

Modular form 182070.2.a.ec

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