Properties

Label 30960.bb
Number of curves $2$
Conductor $30960$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bb1")
 
E.isogeny_class()
 

Elliptic curves in class 30960.bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
30960.bb1 30960bc2 \([0, 0, 0, -180000387, -929519000766]\) \(8000051600110940079507/144453125\) \(11646037440000000\) \([2]\) \(3440640\) \(3.0737\)  
30960.bb2 30960bc1 \([0, 0, 0, -11250387, -14522750766]\) \(1953326569433829507/262451171875\) \(21159225000000000000\) \([2]\) \(1720320\) \(2.7271\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 30960.bb have rank \(0\).

Complex multiplication

The elliptic curves in class 30960.bb do not have complex multiplication.

Modular form 30960.2.a.bb

sage: E.q_eigenform(10)
 
\(q + q^{5} - 4 q^{7} - 4 q^{11} + 2 q^{13} + 6 q^{17} + 6 q^{19} + O(q^{20})\) 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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.