Properties

 Label 2475.c Number of curves $2$ Conductor $2475$ CM no Rank $0$ Graph Related objects

Show commands: SageMath
sage: E = EllipticCurve("c1")

sage: E.isogeny_class()

Elliptic curves in class 2475.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2475.c1 2475d2 $$[1, -1, 1, -3755, -87128]$$ $$19034163/121$$ $$37213171875$$ $$$$ $$1920$$ $$0.86533$$
2475.c2 2475d1 $$[1, -1, 1, -380, 622]$$ $$19683/11$$ $$3383015625$$ $$$$ $$960$$ $$0.51876$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 2475.c have rank $$0$$.

Complex multiplication

The elliptic curves in class 2475.c do not have complex multiplication.

Modular form2475.2.a.c

sage: E.q_eigenform(10)

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels. 