Properties

Label 2370.m
Number of curves $2$
Conductor $2370$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 2370.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2370.m1 2370m2 \([1, 0, 0, -4635130, -3841356970]\) \(-11013097281880624350095521/830805227730\) \(-830805227730\) \([]\) \(51000\) \(2.1820\)  
2370.m2 2370m1 \([1, 0, 0, -3280, -517600]\) \(-3902595313317121/113356365300000\) \(-113356365300000\) \([5]\) \(10200\) \(1.3773\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 2370.m have rank \(0\).

Complex multiplication

The elliptic curves in class 2370.m do not have complex multiplication.

Modular form 2370.2.a.m

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} - 2 q^{7} + q^{8} + q^{9} + q^{10} + 2 q^{11} + q^{12} - q^{13} - 2 q^{14} + q^{15} + q^{16} + 8 q^{17} + q^{18} + 5 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.