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SageMath
E = EllipticCurve("dg1")
E.isogeny_class()
Elliptic curves in class 141120dg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
141120.bl3 | 141120dg1 | \([0, 0, 0, -16023, 389648]\) | \(82881856/36015\) | \(197687478260160\) | \([2]\) | \(589824\) | \(1.4393\) | \(\Gamma_0(N)\)-optimal |
141120.bl2 | 141120dg2 | \([0, 0, 0, -124068, -16551808]\) | \(601211584/11025\) | \(3873060798566400\) | \([2, 2]\) | \(1179648\) | \(1.7858\) | |
141120.bl4 | 141120dg3 | \([0, 0, 0, -588, -48014512]\) | \(-8/354375\) | \(-995929919631360000\) | \([2]\) | \(2359296\) | \(2.1324\) | |
141120.bl1 | 141120dg4 | \([0, 0, 0, -1976268, -1069342288]\) | \(303735479048/105\) | \(295090346557440\) | \([2]\) | \(2359296\) | \(2.1324\) |
Rank
sage: E.rank()
The elliptic curves in class 141120dg have rank \(0\).
Complex multiplication
The elliptic curves in class 141120dg do not have complex multiplication.Modular form 141120.2.a.dg
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.