Properties

Label 30960.s
Number of curves $2$
Conductor $30960$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("s1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 30960.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
30960.s1 30960bn2 \([0, 0, 0, -34203, -2356918]\) \(1481933914201/53916840\) \(160994821570560\) \([2]\) \(110592\) \(1.4958\)  
30960.s2 30960bn1 \([0, 0, 0, -5403, 102602]\) \(5841725401/1857600\) \(5546763878400\) \([2]\) \(55296\) \(1.1492\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 30960.s have rank \(0\).

Complex multiplication

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

Modular form 30960.2.a.s

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