Properties

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

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 30960.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
30960.i1 30960a2 \([0, 0, 0, -663, -6538]\) \(4662947952/26875\) \(185760000\) \([2]\) \(8192\) \(0.42778\)  
30960.i2 30960a1 \([0, 0, 0, -18, -217]\) \(-1492992/46225\) \(-19969200\) \([2]\) \(4096\) \(0.081202\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 30960.2.a.i

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