Properties

Label 79350.dr
Number of curves $4$
Conductor $79350$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("dr1")
 
E.isogeny_class()
 

Elliptic curves in class 79350.dr

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
79350.dr1 79350dv4 \([1, 0, 0, -438023, -111255063]\) \(502270291349/1889568\) \(34965484838244000\) \([2]\) \(985600\) \(2.0338\)  
79350.dr2 79350dv2 \([1, 0, 0, -28048, 1805462]\) \(131872229/18\) \(333080750250\) \([2]\) \(197120\) \(1.2290\)  
79350.dr3 79350dv3 \([1, 0, 0, -14823, -3339063]\) \(-19465109/248832\) \(-4604508291456000\) \([2]\) \(492800\) \(1.6872\)  
79350.dr4 79350dv1 \([1, 0, 0, -1598, 33312]\) \(-24389/12\) \(-222053833500\) \([2]\) \(98560\) \(0.88248\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 79350.dr have rank \(1\).

Complex multiplication

The elliptic curves in class 79350.dr do not have complex multiplication.

Modular form 79350.2.a.dr

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{6} + 2 q^{7} + q^{8} + q^{9} - 2 q^{11} + q^{12} - 6 q^{13} + 2 q^{14} + q^{16} + 2 q^{17} + q^{18} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 5 & 2 & 10 \\ 5 & 1 & 10 & 2 \\ 2 & 10 & 1 & 5 \\ 10 & 2 & 5 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.