Properties

Label 48510p
Number of curves $2$
Conductor $48510$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 48510p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
48510.i2 48510p1 \([1, -1, 0, -94462650, 174845689780]\) \(3168795413730153943/1384979642449920\) \(40743025737735525279989760\) \([2]\) \(15482880\) \(3.6101\) \(\Gamma_0(N)\)-optimal
48510.i1 48510p2 \([1, -1, 0, -734582970, -7542572912204]\) \(1490171974311284012503/26891921826316800\) \(791100626698500685024550400\) \([2]\) \(30965760\) \(3.9567\)  

Rank

sage: E.rank()
 

The elliptic curves in class 48510p have rank \(1\).

Complex multiplication

The elliptic curves in class 48510p do not have complex multiplication.

Modular form 48510.2.a.p

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} - q^{8} + q^{10} - q^{11} + 2 q^{13} + q^{16} + 4 q^{17} + O(q^{20})\) 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.