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Properties

Label 43758n
Number of curves $2$
Conductor $43758$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("n1")
 
E.isogeny_class()
 

Elliptic curves in class 43758n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
43758.p1 43758n1 \([1, -1, 1, -11732195, 36613966115]\) \(-6614510824496145219145875/17618041962927377281024\) \(-475687132999039186587648\) \([3]\) \(4665600\) \(3.2308\) \(\Gamma_0(N)\)-optimal
43758.p2 43758n2 \([1, -1, 1, 102307885, -828078468029]\) \(6016719201015220250419125/18530931219677304938224\) \(-364744319196908393099062992\) \([]\) \(13996800\) \(3.7801\)  

Rank

sage: E.rank()
 

The elliptic curves in class 43758n have rank \(1\).

Complex multiplication

The elliptic curves in class 43758n do not have complex multiplication.

Modular form 43758.2.a.n

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.