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Properties

Label 48510.dg
Number of curves $2$
Conductor $48510$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("dg1")
 
E.isogeny_class()
 

Elliptic curves in class 48510.dg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
48510.dg1 48510ce1 \([1, -1, 1, -1025408, -399354973]\) \(37537160298467283/5519360000\) \(17532373985280000\) \([2]\) \(688128\) \(2.1311\) \(\Gamma_0(N)\)-optimal
48510.dg2 48510ce2 \([1, -1, 1, -931328, -475672669]\) \(-28124139978713043/14526050000000\) \(-46142331924150000000\) \([2]\) \(1376256\) \(2.4777\)  

Rank

sage: E.rank()
 

The elliptic curves in class 48510.dg have rank \(0\).

Complex multiplication

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

Modular form 48510.2.a.dg

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - q^{5} + q^{8} - q^{10} + q^{11} + 4 q^{13} + q^{16} + 2 q^{17} + 6 q^{19} + O(q^{20})\) 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 LMFDB 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 LMFDB labels.