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Properties

Label 18515m
Number of curves $2$
Conductor $18515$
CM no
Rank $0$
Graph

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

Elliptic curves in class 18515m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
18515.g1 18515m1 \([1, -1, 1, -86062, 9735724]\) \(476196576129/197225\) \(29196378208025\) \([2]\) \(76032\) \(1.5457\) \(\Gamma_0(N)\)-optimal
18515.g2 18515m2 \([1, -1, 1, -72837, 12819794]\) \(-288673724529/311181605\) \(-46066045536621845\) \([2]\) \(152064\) \(1.8923\)  

Rank

sage: E.rank()
 

The elliptic curves in class 18515m have rank \(0\).

Complex multiplication

The elliptic curves in class 18515m do not have complex multiplication.

Modular form 18515.2.a.m

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