Properties

Label 20280.b
Number of curves $4$
Conductor $20280$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 20280.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
20280.b1 20280d4 \([0, -1, 0, -1406136, 642253260]\) \(31103978031362/195\) \(1927634442240\) \([2]\) \(258048\) \(1.9629\)  
20280.b2 20280d3 \([0, -1, 0, -121736, 1648620]\) \(20183398562/11567205\) \(114345347479234560\) \([2]\) \(258048\) \(1.9629\)  
20280.b3 20280d2 \([0, -1, 0, -87936, 10044540]\) \(15214885924/38025\) \(187944358118400\) \([2, 2]\) \(129024\) \(1.6163\)  
20280.b4 20280d1 \([0, -1, 0, -3436, 276340]\) \(-3631696/24375\) \(-30119288160000\) \([2]\) \(64512\) \(1.2697\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 20280.b have rank \(1\).

Complex multiplication

The elliptic curves in class 20280.b do not have complex multiplication.

Modular form 20280.2.a.b

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} - 4q^{7} + q^{9} - 4q^{11} + q^{15} + 6q^{17} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.