Properties

Label 301530d
Number of curves $4$
Conductor $301530$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 301530d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
301530.d3 301530d1 \([1, 1, 0, -30428, 1777152]\) \(21047437081/2831760\) \(419202109034640\) \([2]\) \(1351680\) \(1.5332\) \(\Gamma_0(N)\)-optimal
301530.d2 301530d2 \([1, 1, 0, -125648, -15381492]\) \(1481933914201/171872100\) \(25443239117796900\) \([2, 2]\) \(2703360\) \(1.8798\)  
301530.d4 301530d3 \([1, 1, 0, 175882, -77556978]\) \(4064592619079/19938671250\) \(-2951638923972491250\) \([2]\) \(5406720\) \(2.2263\)  
301530.d1 301530d4 \([1, 1, 0, -1950698, -1049454822]\) \(5545326987531001/89921490\) \(13311607712354610\) \([2]\) \(5406720\) \(2.2263\)  

Rank

sage: E.rank()
 

The elliptic curves in class 301530d have rank \(0\).

Complex multiplication

The elliptic curves in class 301530d do not have complex multiplication.

Modular form 301530.2.a.d

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} - q^{8} + q^{9} + q^{10} - q^{12} + 2 q^{13} + q^{15} + q^{16} + 6 q^{17} - q^{18} - q^{19} + O(q^{20})\) 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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.