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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 27753.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
27753.c1 | 27753d4 | \([1, 0, 0, -123224, 16622493]\) | \(347873904937/395307\) | \(235137822554547\) | \([2]\) | \(145152\) | \(1.6710\) | |
27753.c2 | 27753d2 | \([1, 0, 0, -9689, 114504]\) | \(169112377/88209\) | \(52468770322089\) | \([2, 2]\) | \(72576\) | \(1.3244\) | |
27753.c3 | 27753d1 | \([1, 0, 0, -5484, -155457]\) | \(30664297/297\) | \(176662526337\) | \([2]\) | \(36288\) | \(0.97787\) | \(\Gamma_0(N)\)-optimal |
27753.c4 | 27753d3 | \([1, 0, 0, 36566, 900839]\) | \(9090072503/5845851\) | \(-3477248505891171\) | \([2]\) | \(145152\) | \(1.6710\) |
Rank
sage: E.rank()
The elliptic curves in class 27753.c have rank \(0\).
Complex multiplication
The elliptic curves in class 27753.c do not have complex multiplication.Modular form 27753.2.a.c
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.