Properties

Label 301180a
Number of curves $4$
Conductor $301180$
CM no
Rank $2$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 301180a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
301180.a4 301180a1 \([0, 1, 0, -62061, 5808160]\) \(643956736/15125\) \(620905790978000\) \([2]\) \(1866240\) \(1.6240\) \(\Gamma_0(N)\)-optimal
301180.a3 301180a2 \([0, 1, 0, -137356, -11118156]\) \(436334416/171875\) \(112891961996000000\) \([2]\) \(3732480\) \(1.9706\)  
301180.a2 301180a3 \([0, 1, 0, -609661, -181115100]\) \(610462990336/8857805\) \(363627267428355920\) \([2]\) \(5598720\) \(2.1733\)  
301180.a1 301180a4 \([0, 1, 0, -9720356, -11667879356]\) \(154639330142416/33275\) \(21855883842425600\) \([2]\) \(11197440\) \(2.5199\)  

Rank

sage: E.rank()
 

The elliptic curves in class 301180a have rank \(2\).

Complex multiplication

The elliptic curves in class 301180a do not have complex multiplication.

Modular form 301180.2.a.a

sage: E.q_eigenform(10)
 
\(q - 2q^{3} - q^{5} - 4q^{7} + q^{9} - q^{11} + 4q^{13} + 2q^{15} + 4q^{19} + O(q^{20})\)  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 Cremona 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 Cremona labels.