Properties

 Label 4275.p Number of curves $2$ Conductor $4275$ CM no Rank $0$ Graph

Related objects

Show commands: SageMath
E = EllipticCurve("p1")

E.isogeny_class()

Elliptic curves in class 4275.p

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4275.p1 4275o2 $$[1, -1, 0, -222, -1189]$$ $$13312053/361$$ $$32896125$$ $$[2]$$ $$1024$$ $$0.22265$$
4275.p2 4275o1 $$[1, -1, 0, 3, -64]$$ $$27/19$$ $$-1731375$$ $$[2]$$ $$512$$ $$-0.12393$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 4275.p have rank $$0$$.

Complex multiplication

The elliptic curves in class 4275.p do not have complex multiplication.

Modular form4275.2.a.p

sage: E.q_eigenform(10)

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

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.