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Properties

Label 42350bc
Number of curves $2$
Conductor $42350$
CM no
Rank $1$
Graph

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

Elliptic curves in class 42350bc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
42350.g2 42350bc1 \([1, 0, 1, -10651, 931698]\) \(-4826809/10780\) \(-298397305937500\) \([2]\) \(184320\) \(1.4661\) \(\Gamma_0(N)\)-optimal
42350.g1 42350bc2 \([1, 0, 1, -222401, 40317198]\) \(43949604889/42350\) \(1172275130468750\) \([2]\) \(368640\) \(1.8127\)  

Rank

sage: E.rank()
 

The elliptic curves in class 42350bc have rank \(1\).

Complex multiplication

The elliptic curves in class 42350bc do not have complex multiplication.

Modular form 42350.2.a.bc

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