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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 106742g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 106742.k2 | 106742g1 | \([1, 1, 1, -43598, 3486819]\) | \(-413493625/152\) | \(-3368982891608\) | \([]\) | \(302328\) | \(1.3717\) | \(\Gamma_0(N)\)-optimal |
| 106742.k3 | 106742g2 | \([1, 1, 1, 26627, 13329555]\) | \(94196375/3511808\) | \(-77836980727711232\) | \([]\) | \(906984\) | \(1.9210\) | |
| 106742.k1 | 106742g3 | \([1, 1, 1, -240228, -364643867]\) | \(-69173457625/2550136832\) | \(-56522153672812003328\) | \([]\) | \(2720952\) | \(2.4703\) |
Rank
sage: E.rank()
The elliptic curves in class 106742g have rank \(0\).
Complex multiplication
The elliptic curves in class 106742g do not have complex multiplication.Modular form 106742.2.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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
