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Properties

Label 95370.de
Number of curves $2$
Conductor $95370$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("de1")
 
E.isogeny_class()
 

Elliptic curves in class 95370.de

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
95370.de1 95370cz2 \([1, 0, 0, -254326, 44902556]\) \(75370704203521/7497765000\) \(180977820033285000\) \([2]\) \(1327104\) \(2.0479\)  
95370.de2 95370cz1 \([1, 0, 0, -57806, -4581180]\) \(885012508801/137332800\) \(3314879935963200\) \([2]\) \(663552\) \(1.7014\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 95370.de have rank \(1\).

Complex multiplication

The elliptic curves in class 95370.de do not have complex multiplication.

Modular form 95370.2.a.de

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} + 2 q^{7} + q^{8} + q^{9} - q^{10} - q^{11} + q^{12} - 4 q^{13} + 2 q^{14} - q^{15} + q^{16} + q^{18} - 2 q^{19} + O(q^{20})\) 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.