Properties

Label 77315.d
Number of curves $3$
Conductor $77315$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 77315.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
77315.d1 77315f3 \([0, 1, 1, -290115, 62820994]\) \(-250523582464/13671875\) \(-147372084576171875\) \([]\) \(613548\) \(2.0525\)  
77315.d2 77315f1 \([0, 1, 1, -2945, -69236]\) \(-262144/35\) \(-377272536515\) \([]\) \(68172\) \(0.95392\) \(\Gamma_0(N)\)-optimal
77315.d3 77315f2 \([0, 1, 1, 19145, 180381]\) \(71991296/42875\) \(-462158857230875\) \([]\) \(204516\) \(1.5032\)  

Rank

sage: E.rank()
 

The elliptic curves in class 77315.d have rank \(0\).

Complex multiplication

The elliptic curves in class 77315.d do not have complex multiplication.

Modular form 77315.2.a.d

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2q^{4} + q^{5} + q^{7} - 2q^{9} + 3q^{11} - 2q^{12} - 5q^{13} + q^{15} + 4q^{16} + 3q^{17} - 2q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.