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Properties

Label 141610c
Number of curves $2$
Conductor $141610$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 141610c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
141610.br1 141610c1 \([1, -1, 1, -1864827, 980649471]\) \(-5154200289/20\) \(-2782965638175380\) \([]\) \(4139520\) \(2.1767\) \(\Gamma_0(N)\)-optimal
141610.br2 141610c2 \([1, -1, 1, 13004223, -9303380271]\) \(1747829720511/1280000000\) \(-178109800843224320000000\) \([]\) \(28976640\) \(3.1497\)  

Rank

sage: E.rank()
 

The elliptic curves in class 141610c have rank \(1\).

Complex multiplication

The elliptic curves in class 141610c do not have complex multiplication.

Modular form 141610.2.a.c

sage: E.q_eigenform(10)
 
\(q + q^{2} - 3 q^{3} + q^{4} + q^{5} - 3 q^{6} + q^{8} + 6 q^{9} + q^{10} + 2 q^{11} - 3 q^{12} - 3 q^{15} + q^{16} + 6 q^{18} - 6 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.