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SageMath
E = EllipticCurve("ej1")
E.isogeny_class()
Elliptic curves in class 159120.ej
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
159120.ej1 | 159120w4 | \([0, 0, 0, -150627, -22498526]\) | \(126574061279329/16286595\) | \(48631512084480\) | \([2]\) | \(917504\) | \(1.6474\) | |
159120.ej2 | 159120w2 | \([0, 0, 0, -10227, -287246]\) | \(39616946929/10989225\) | \(32813650022400\) | \([2, 2]\) | \(458752\) | \(1.3008\) | |
159120.ej3 | 159120w1 | \([0, 0, 0, -3747, 84706]\) | \(1948441249/89505\) | \(267260497920\) | \([2]\) | \(229376\) | \(0.95426\) | \(\Gamma_0(N)\)-optimal |
159120.ej4 | 159120w3 | \([0, 0, 0, 26493, -1880894]\) | \(688699320191/910381875\) | \(-2718385712640000\) | \([4]\) | \(917504\) | \(1.6474\) |
Rank
sage: E.rank()
The elliptic curves in class 159120.ej have rank \(0\).
Complex multiplication
The elliptic curves in class 159120.ej do not have complex multiplication.Modular form 159120.2.a.ej
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.