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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 81120t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
81120.bd3 | 81120t1 | \([0, 1, 0, -5126, -137760]\) | \(48228544/2025\) | \(625554446400\) | \([2, 2]\) | \(147456\) | \(1.0282\) | \(\Gamma_0(N)\)-optimal |
81120.bd4 | 81120t2 | \([0, 1, 0, 2479, -504321]\) | \(85184/5625\) | \(-111209679360000\) | \([2]\) | \(294912\) | \(1.3748\) | |
81120.bd2 | 81120t3 | \([0, 1, 0, -13576, 423320]\) | \(111980168/32805\) | \(81071856253440\) | \([2]\) | \(294912\) | \(1.3748\) | |
81120.bd1 | 81120t4 | \([0, 1, 0, -81176, -8929140]\) | \(23937672968/45\) | \(111209679360\) | \([2]\) | \(294912\) | \(1.3748\) |
Rank
sage: E.rank()
The elliptic curves in class 81120t have rank \(2\).
Complex multiplication
The elliptic curves in class 81120t do not have complex multiplication.Modular form 81120.2.a.t
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.