Properties

Label 21780.l
Number of curves $4$
Conductor $21780$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("l1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 21780.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
21780.l1 21780n4 \([0, 0, 0, -7732263, -8275761362]\) \(154639330142416/33275\) \(11001240747129600\) \([2]\) \(622080\) \(2.4627\)  
21780.l2 21780n3 \([0, 0, 0, -484968, -128352323]\) \(610462990336/8857805\) \(183033142930368720\) \([2]\) \(311040\) \(2.1161\)  
21780.l3 21780n2 \([0, 0, 0, -109263, -7855562]\) \(436334416/171875\) \(56824590636000000\) \([2]\) \(207360\) \(1.9134\)  
21780.l4 21780n1 \([0, 0, 0, -49368, 4135417]\) \(643956736/15125\) \(312535248498000\) \([2]\) \(103680\) \(1.5668\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 21780.l have rank \(0\).

Complex multiplication

The elliptic curves in class 21780.l do not have complex multiplication.

Modular form 21780.2.a.l

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

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.