Properties

 Label 5880.p Number of curves $4$ Conductor $5880$ CM no Rank $1$ Graph

Learn more

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

E.isogeny_class()

Elliptic curves in class 5880.p

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5880.p1 5880g4 $$[0, -1, 0, -10600, 423340]$$ $$546718898/405$$ $$97582786560$$ $$[2]$$ $$9216$$ $$1.0424$$
5880.p2 5880g3 $$[0, -1, 0, -6680, -205428]$$ $$136835858/1875$$ $$451772160000$$ $$[2]$$ $$9216$$ $$1.0424$$
5880.p3 5880g2 $$[0, -1, 0, -800, 3900]$$ $$470596/225$$ $$27106329600$$ $$[2, 2]$$ $$4608$$ $$0.69578$$
5880.p4 5880g1 $$[0, -1, 0, 180, 372]$$ $$21296/15$$ $$-451772160$$ $$[2]$$ $$2304$$ $$0.34921$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 5880.p have rank $$1$$.

Complex multiplication

The elliptic curves in class 5880.p do not have complex multiplication.

Modular form5880.2.a.p

sage: E.q_eigenform(10)

$$q - q^{3} + q^{5} + q^{9} + 6 q^{13} - q^{15} + 2 q^{17} - 4 q^{19} + O(q^{20})$$

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.