Properties

Label 60840u
Number of curves $2$
Conductor $60840$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 60840u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
60840.bu2 60840u1 \([0, 0, 0, -507, -2851706]\) \(-4/975\) \(-3513113770982400\) \([2]\) \(258048\) \(1.6618\) \(\Gamma_0(N)\)-optimal
60840.bu1 60840u2 \([0, 0, 0, -304707, -63752546]\) \(434163602/7605\) \(54804574827325440\) \([2]\) \(516096\) \(2.0084\)  

Rank

sage: E.rank()
 

The elliptic curves in class 60840u have rank \(1\).

Complex multiplication

The elliptic curves in class 60840u do not have complex multiplication.

Modular form 60840.2.a.u

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

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.