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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 143745g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
143745.j3 | 143745g1 | \([1, 0, 0, -3451, 73640]\) | \(1771561/105\) | \(269401272945\) | \([2]\) | \(207360\) | \(0.94635\) | \(\Gamma_0(N)\)-optimal |
143745.j2 | 143745g2 | \([1, 0, 0, -10296, -311049]\) | \(47045881/11025\) | \(28287133659225\) | \([2, 2]\) | \(414720\) | \(1.2929\) | |
143745.j4 | 143745g3 | \([1, 0, 0, 23929, -1933314]\) | \(590589719/972405\) | \(-2494925188743645\) | \([2]\) | \(829440\) | \(1.6395\) | |
143745.j1 | 143745g4 | \([1, 0, 0, -154041, -23281500]\) | \(157551496201/13125\) | \(33675159118125\) | \([2]\) | \(829440\) | \(1.6395\) |
Rank
sage: E.rank()
The elliptic curves in class 143745g have rank \(1\).
Complex multiplication
The elliptic curves in class 143745g do not have complex multiplication.Modular form 143745.2.a.g
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.