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Properties

Label 333270.dg
Number of curves $2$
Conductor $333270$
CM no
Rank $0$
Graph

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

Elliptic curves in class 333270.dg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
333270.dg1 333270dg2 \([1, -1, 1, -94316303, -309312496169]\) \(70665260180607/9411920000\) \(12358230168200615601840000\) \([2]\) \(94961664\) \(3.5424\)  
333270.dg2 333270dg1 \([1, -1, 1, -24234383, 41013005527]\) \(1198785674367/140492800\) \(184472706883927556505600\) \([2]\) \(47480832\) \(3.1958\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 333270.dg have rank \(0\).

Complex multiplication

The elliptic curves in class 333270.dg do not have complex multiplication.

Modular form 333270.2.a.dg

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - q^{5} - q^{7} + q^{8} - q^{10} + 2 q^{11} - 4 q^{13} - q^{14} + q^{16} + 6 q^{17} + 4 q^{19} + O(q^{20})\) 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.