Properties

 Label 2415.h Number of curves $4$ Conductor $2415$ CM no Rank $0$ Graph Related objects

Show commands: SageMath
sage: E = EllipticCurve("h1")

sage: E.isogeny_class()

Elliptic curves in class 2415.h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2415.h1 2415e3 $$[1, 0, 1, -4294, 107927]$$ $$8753151307882969/65205$$ $$65205$$ $$$$ $$1408$$ $$0.51833$$
2415.h2 2415e2 $$[1, 0, 1, -269, 1667]$$ $$2141202151369/5832225$$ $$5832225$$ $$[2, 2]$$ $$704$$ $$0.17176$$
2415.h3 2415e4 $$[1, 0, 1, -164, 3011]$$ $$-483551781049/3672913125$$ $$-3672913125$$ $$$$ $$1408$$ $$0.51833$$
2415.h4 2415e1 $$[1, 0, 1, -24, 1]$$ $$1439069689/828345$$ $$828345$$ $$$$ $$352$$ $$-0.17481$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 2415.h have rank $$0$$.

Complex multiplication

The elliptic curves in class 2415.h do not have complex multiplication.

Modular form2415.2.a.h

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with LMFDB labels. 