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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 11154u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
11154.s2 | 11154u1 | \([1, 0, 1, 2193, -87878]\) | \(241804367/833976\) | \(-4025442862584\) | \([]\) | \(40320\) | \(1.1017\) | \(\Gamma_0(N)\)-optimal |
11154.s1 | 11154u2 | \([1, 0, 1, -104277, -12992042]\) | \(-25979045828113/52635726\) | \(-254062595978334\) | \([]\) | \(120960\) | \(1.6510\) |
Rank
sage: E.rank()
The elliptic curves in class 11154u have rank \(1\).
Complex multiplication
The elliptic curves in class 11154u do not have complex multiplication.Modular form 11154.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.