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Properties

Label 248430.c
Number of curves $2$
Conductor $248430$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 248430.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
248430.c1 248430c2 \([1, 1, 0, -151613658337768, 718547637921841722688]\) \(-23763856998804796987128199384369/7318708992000\) \(-118701509591867019645364992000\) \([]\) \(18681062400\) \(6.3357\)  
248430.c2 248430c1 \([1, 1, 0, -1871470193128, 985996832485072192]\) \(-44694151057272491356949809/30197762286189281280\) \(-489774900680600406067833570884321280\) \([]\) \(6227020800\) \(5.7864\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 248430.c have rank \(0\).

Complex multiplication

The elliptic curves in class 248430.c do not have complex multiplication.

Modular form 248430.2.a.c

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.