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SageMath
E = EllipticCurve("iu1")
E.isogeny_class()
Elliptic curves in class 446160iu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
446160.iu2 | 446160iu1 | \([0, 1, 0, -2724931720, 54857394106100]\) | \(-113180217375258301213009/260161419375000000\) | \(-5143549872095331840000000000\) | \([2]\) | \(325140480\) | \(4.1985\) | \(\Gamma_0(N)\)-optimal* |
446160.iu1 | 446160iu2 | \([0, 1, 0, -43622931720, 3506861263706100]\) | \(464352938845529653759213009/2445173327025000\) | \(48342567409435497369600000\) | \([2]\) | \(650280960\) | \(4.5451\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 446160iu have rank \(1\).
Complex multiplication
The elliptic curves in class 446160iu do not have complex multiplication.Modular form 446160.2.a.iu
sage: E.q_eigenform(10)
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.