Properties

Label 177870im
Number of curves $2$
Conductor $177870$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("im1")
 
E.isogeny_class()
 

Elliptic curves in class 177870im

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
177870.n1 177870im1 \([1, 1, 0, -23745768, 30354458688]\) \(20713044141847/6415200000\) \(458615439692204810400000\) \([2]\) \(25804800\) \(3.2447\) \(\Gamma_0(N)\)-optimal
177870.n2 177870im2 \([1, 1, 0, 65900712, 205147165392]\) \(442746922510313/510468750000\) \(-36492837359767454531250000\) \([2]\) \(51609600\) \(3.5913\)  

Rank

sage: E.rank()
 

The elliptic curves in class 177870im have rank \(1\).

Complex multiplication

The elliptic curves in class 177870im do not have complex multiplication.

Modular form 177870.2.a.im

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