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Properties

Label 308550bc
Number of curves $2$
Conductor $308550$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bc1")
 
E.isogeny_class()
 

Elliptic curves in class 308550bc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
308550.bc1 308550bc1 \([1, 1, 0, -310125, -67809375]\) \(-119168121961/2524500\) \(-69879777257812500\) \([]\) \(4147200\) \(2.0226\) \(\Gamma_0(N)\)-optimal
308550.bc2 308550bc2 \([1, 1, 0, 1278000, -304440000]\) \(8339492177639/6277634880\) \(-173768955088245000000\) \([]\) \(12441600\) \(2.5719\)  

Rank

sage: E.rank()
 

The elliptic curves in class 308550bc have rank \(0\).

Complex multiplication

The elliptic curves in class 308550bc do not have complex multiplication.

Modular form 308550.2.a.bc

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.