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Properties

Label 28314.bz
Number of curves $2$
Conductor $28314$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bz1")
 
E.isogeny_class()
 

Elliptic curves in class 28314.bz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
28314.bz1 28314cc1 \([1, -1, 1, -6288322712, 192138899879963]\) \(-21293376668673906679951249/26211168887701209984\) \(-33850885048515470736879002496\) \([]\) \(33868800\) \(4.3841\) \(\Gamma_0(N)\)-optimal
28314.bz2 28314cc2 \([1, -1, 1, 17808513898, -12058462656159037]\) \(483641001192506212470106511/48918776756543177755473774\) \(-63177033263737225236667693540545006\) \([]\) \(237081600\) \(5.3570\)  

Rank

sage: E.rank()
 

The elliptic curves in class 28314.bz have rank \(1\).

Complex multiplication

The elliptic curves in class 28314.bz do not have complex multiplication.

Modular form 28314.2.a.bz

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{5} - q^{7} + q^{8} + q^{10} + q^{13} - q^{14} + q^{16} + 4 q^{17} - 6 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.