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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 154.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
154.c1 | 154b3 | \([1, -1, 1, -5164, -141529]\) | \(15226621995131793/2324168\) | \(2324168\) | \([2]\) | \(96\) | \(0.62717\) | |
154.c2 | 154b4 | \([1, -1, 1, -604, 2343]\) | \(24331017010833/12004097336\) | \(12004097336\) | \([2]\) | \(96\) | \(0.62717\) | |
154.c3 | 154b2 | \([1, -1, 1, -324, -2137]\) | \(3750606459153/45914176\) | \(45914176\) | \([2, 2]\) | \(48\) | \(0.28060\) | |
154.c4 | 154b1 | \([1, -1, 1, -4, -89]\) | \(-5545233/3469312\) | \(-3469312\) | \([4]\) | \(24\) | \(-0.065974\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 154.c have rank \(0\).
Complex multiplication
The elliptic curves in class 154.c do not have complex multiplication.Modular form 154.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.