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Properties

Label 76230eq
Number of curves $2$
Conductor $76230$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("eq1")
 
E.isogeny_class()
 

Elliptic curves in class 76230eq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
76230.dw1 76230eq1 \([1, -1, 1, -463937, 121996361]\) \(-584043889/1400\) \(-26471735547780600\) \([]\) \(1140480\) \(2.0306\) \(\Gamma_0(N)\)-optimal
76230.dw2 76230eq2 \([1, -1, 1, 853753, 613758269]\) \(3639707951/10718750\) \(-202674225287695218750\) \([]\) \(3421440\) \(2.5799\)  

Rank

sage: E.rank()
 

The elliptic curves in class 76230eq have rank \(1\).

Complex multiplication

The elliptic curves in class 76230eq do not have complex multiplication.

Modular form 76230.2.a.eq

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