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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 15210.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
15210.u1 | 15210s2 | \([1, -1, 0, -1296684, 568650928]\) | \(68523370149961/243360\) | \(856321481676960\) | \([2]\) | \(215040\) | \(2.0836\) | |
15210.u2 | 15210s1 | \([1, -1, 0, -79884, 9166288]\) | \(-16022066761/998400\) | \(-3513113770982400\) | \([2]\) | \(107520\) | \(1.7370\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 15210.u have rank \(1\).
Complex multiplication
The elliptic curves in class 15210.u do not have complex multiplication.Modular form 15210.2.a.u
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 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.