Properties

 Label 2475h Number of curves $3$ Conductor $2475$ CM no Rank $0$ Graph Related objects

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

sage: E.isogeny_class()

Elliptic curves in class 2475h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2475.a3 2475h1 $$[0, 0, 1, -75, -594]$$ $$-4096/11$$ $$-125296875$$ $$[]$$ $$840$$ $$0.24130$$ $$\Gamma_0(N)$$-optimal
2475.a2 2475h2 $$[0, 0, 1, -2325, 78156]$$ $$-122023936/161051$$ $$-1834471546875$$ $$[]$$ $$4200$$ $$1.0460$$
2475.a1 2475h3 $$[0, 0, 1, -1759575, 898379406]$$ $$-52893159101157376/11$$ $$-125296875$$ $$[]$$ $$21000$$ $$1.8507$$

Rank

sage: E.rank()

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

Complex multiplication

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

Modular form2475.2.a.h

sage: E.q_eigenform(10)

$$q - 2 q^{2} + 2 q^{4} + 2 q^{7} - q^{11} - 4 q^{13} - 4 q^{14} - 4 q^{16} - 2 q^{17} + O(q^{20})$$ 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 Cremona numbering.

$$\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with Cremona labels. 