Properties

Label 302330.c
Number of curves $2$
Conductor $302330$
CM no
Rank $0$
Graph

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

Elliptic curves in class 302330.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
302330.c1 302330c2 \([1, 0, 1, -13809059, -19752821154]\) \(-50516307977225837929/1293942784000\) \(-7459322655145984000\) \([]\) \(23587200\) \(2.7285\)  
302330.c2 302330c1 \([1, 0, 1, -53044, -63519438]\) \(-2863099371769/300652944640\) \(-1733204395913616640\) \([3]\) \(7862400\) \(2.1792\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 302330.c have rank \(0\).

Complex multiplication

The elliptic curves in class 302330.c do not have complex multiplication.

Modular form 302330.2.a.c

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