Properties

Label 28980.h
Number of curves $2$
Conductor $28980$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("h1")
 
E.isogeny_class()
 

Elliptic curves in class 28980.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
28980.h1 28980j1 \([0, 0, 0, -90912, -10550059]\) \(7124261256822784/475453125\) \(5545685250000\) \([2]\) \(138240\) \(1.5009\) \(\Gamma_0(N)\)-optimal
28980.h2 28980j2 \([0, 0, 0, -85287, -11912434]\) \(-367624742361424/115740505125\) \(-21599956028448000\) \([2]\) \(276480\) \(1.8475\)  

Rank

sage: E.rank()
 

The elliptic curves in class 28980.h have rank \(0\).

Complex multiplication

The elliptic curves in class 28980.h do not have complex multiplication.

Modular form 28980.2.a.h

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