Properties

Label 308550.dp
Number of curves $2$
Conductor $308550$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("dp1")
 
E.isogeny_class()
 

Elliptic curves in class 308550.dp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
308550.dp1 308550dp2 \([1, 0, 1, -2175303276, 38903128502698]\) \(41125104693338423360329/179205840000000000\) \(4960532454941250000000000000\) \([2]\) \(287539200\) \(4.1673\)  
308550.dp2 308550dp1 \([1, 0, 1, -68935276, 1207566774698]\) \(-1308796492121439049/22000592486400000\) \(-608990494153113600000000000\) \([2]\) \(143769600\) \(3.8207\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 308550.dp have rank \(0\).

Complex multiplication

The elliptic curves in class 308550.dp do not have complex multiplication.

Modular form 308550.2.a.dp

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} - 2 q^{7} - q^{8} + q^{9} + q^{12} + 2 q^{14} + q^{16} + q^{17} - q^{18} + 8 q^{19} + O(q^{20})\) 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.