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Properties

Label 77315.g
Number of curves $2$
Conductor $77315$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 77315.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
77315.g1 77315g2 \([1, -1, 0, -3821984, 2874935115]\) \(5517084663/4375\) \(4896195819824605625\) \([2]\) \(2129664\) \(2.5167\)  
77315.g2 77315g1 \([1, -1, 0, -188179, 64550328]\) \(-658503/1225\) \(-1370934829550889575\) \([2]\) \(1064832\) \(2.1701\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 77315.2.a.g

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{4} + q^{5} + q^{7} - 3 q^{8} - 3 q^{9} + q^{10} + 6 q^{11} - 2 q^{13} + q^{14} - q^{16} - 2 q^{17} - 3 q^{18} + 8 q^{19} + O(q^{20})\) 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.