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Properties

Label 360030bc
Number of curves $4$
Conductor $360030$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("bc1")
 
E.isogeny_class()
 

Elliptic curves in class 360030bc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
360030.bc4 360030bc1 \([1, 0, 0, -187750, -31187500]\) \(731920133376459036001/3797191406250000\) \(3797191406250000\) \([4]\) \(6168576\) \(1.8350\) \(\Gamma_0(N)\)-optimal
360030.bc2 360030bc2 \([1, 0, 0, -3000250, -2000500000]\) \(2986730620428096864036001/81013500562500\) \(81013500562500\) \([2, 2]\) \(12337152\) \(2.1815\)  
360030.bc3 360030bc3 \([1, 0, 0, -2996500, -2005749250]\) \(-2975545306089301103496001/15557184648036000750\) \(-15557184648036000750\) \([2]\) \(24674304\) \(2.5281\)  
360030.bc1 360030bc4 \([1, 0, 0, -48004000, -128020000750]\) \(12233648382354948213504576001/9000750\) \(9000750\) \([2]\) \(24674304\) \(2.5281\)  

Rank

sage: E.rank()
 

The elliptic curves in class 360030bc have rank \(0\).

Complex multiplication

The elliptic curves in class 360030bc do not have complex multiplication.

Modular form 360030.2.a.bc

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} + 4 q^{7} + q^{8} + q^{9} + q^{10} - q^{11} + q^{12} + 6 q^{13} + 4 q^{14} + q^{15} + q^{16} + 2 q^{17} + q^{18} + 8 q^{19} + O(q^{20})\) 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.