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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 11154o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
11154.n2 | 11154o1 | \([1, 0, 1, -56112, -13125890]\) | \(-4047806261953/13066420224\) | \(-63069114734985216\) | \([2]\) | \(169344\) | \(1.9100\) | \(\Gamma_0(N)\)-optimal |
11154.n1 | 11154o2 | \([1, 0, 1, -1245872, -534716674]\) | \(44308125149913793/61165323648\) | \(295233334672079232\) | \([2]\) | \(338688\) | \(2.2566\) |
Rank
sage: E.rank()
The elliptic curves in class 11154o have rank \(0\).
Complex multiplication
The elliptic curves in class 11154o do not have complex multiplication.Modular form 11154.2.a.o
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.