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Properties

Label 28322.d
Number of curves $2$
Conductor $28322$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 28322.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
28322.d1 28322i1 \([1, 0, 1, -1307, -20688]\) \(-208537/34\) \(-40213189954\) \([]\) \(34560\) \(0.76236\) \(\Gamma_0(N)\)-optimal
28322.d2 28322i2 \([1, 0, 1, 8808, 80462]\) \(63905303/39304\) \(-46486447586824\) \([]\) \(103680\) \(1.3117\)  

Rank

sage: E.rank()
 

The elliptic curves in class 28322.d have rank \(0\).

Complex multiplication

The elliptic curves in class 28322.d do not have complex multiplication.

Modular form 28322.2.a.d

sage: E.q_eigenform(10)
 
\(q - q^{2} - 2 q^{3} + q^{4} + 3 q^{5} + 2 q^{6} - q^{8} + q^{9} - 3 q^{10} - 2 q^{12} - 2 q^{13} - 6 q^{15} + q^{16} - q^{18} + 7 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.