Properties

Label 30960.y
Number of curves $2$
Conductor $30960$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("y1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 30960.y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
30960.y1 30960v2 \([0, 0, 0, -1323, 18458]\) \(2315685267/9245\) \(1022423040\) \([2]\) \(16384\) \(0.58555\)  
30960.y2 30960v1 \([0, 0, 0, -123, -22]\) \(1860867/1075\) \(118886400\) \([2]\) \(8192\) \(0.23898\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 30960.y have rank \(1\).

Complex multiplication

The elliptic curves in class 30960.y do not have complex multiplication.

Modular form 30960.2.a.y

sage: E.q_eigenform(10)
 
\(q - q^{5} + 4q^{7} + 2q^{13} - 2q^{17} - 6q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.