Properties

Label 882.i
Number of curves $6$
Conductor $882$
CM no
Rank $0$
Graph

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

Elliptic curves in class 882.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
882.i1 882i6 \([1, -1, 1, -1204160, -508296477]\) \(2251439055699625/25088\) \(2151700443648\) \([2]\) \(6912\) \(1.9354\)  
882.i2 882i5 \([1, -1, 1, -75200, -7941405]\) \(-548347731625/1835008\) \(-157381518163968\) \([2]\) \(3456\) \(1.5888\)  
882.i3 882i4 \([1, -1, 1, -15665, -614631]\) \(4956477625/941192\) \(80722386956232\) \([2]\) \(2304\) \(1.3861\)  
882.i4 882i2 \([1, -1, 1, -4640, 122721]\) \(128787625/98\) \(8405079858\) \([2]\) \(768\) \(0.83675\)  
882.i5 882i1 \([1, -1, 1, -230, 2769]\) \(-15625/28\) \(-2401451388\) \([2]\) \(384\) \(0.49018\) \(\Gamma_0(N)\)-optimal
882.i6 882i3 \([1, -1, 1, 1975, -57207]\) \(9938375/21952\) \(-1882737888192\) \([2]\) \(1152\) \(1.0395\)  

Rank

sage: E.rank()
 

The elliptic curves in class 882.i have rank \(0\).

Complex multiplication

The elliptic curves in class 882.i do not have complex multiplication.

Modular form 882.2.a.i

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{8} + 4q^{13} + q^{16} + 6q^{17} - 2q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 9 & 18 & 6 \\ 2 & 1 & 6 & 18 & 9 & 3 \\ 3 & 6 & 1 & 3 & 6 & 2 \\ 9 & 18 & 3 & 1 & 2 & 6 \\ 18 & 9 & 6 & 2 & 1 & 3 \\ 6 & 3 & 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.