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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 106782.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
106782.l1 | 106782j4 | \([1, 1, 1, -28392404, 58218777317]\) | \(986551739719628473/111045168\) | \(284911520129441712\) | \([2]\) | \(8294400\) | \(2.7735\) | |
106782.l2 | 106782j3 | \([1, 1, 1, -3202804, -749594395]\) | \(1416134368422073/725251155408\) | \(1860796042588068769872\) | \([2]\) | \(8294400\) | \(2.7735\) | |
106782.l3 | 106782j2 | \([1, 1, 1, -1779044, 904245221]\) | \(242702053576633/2554695936\) | \(6554650829960173824\) | \([2, 2]\) | \(4147200\) | \(2.4270\) | |
106782.l4 | 106782j1 | \([1, 1, 1, -26724, 35094501]\) | \(-822656953/207028224\) | \(-531177781725167616\) | \([2]\) | \(2073600\) | \(2.0804\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 106782.l have rank \(0\).
Complex multiplication
The elliptic curves in class 106782.l do not have complex multiplication.Modular form 106782.2.a.l
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.