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SageMath
E = EllipticCurve("dg1")
E.isogeny_class()
Elliptic curves in class 164934dg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 164934.w1 | 164934dg1 | \([1, -1, 0, -87327, 9954265]\) | \(858729462625/38148\) | \(3271805983908\) | \([2]\) | \(737280\) | \(1.4787\) | \(\Gamma_0(N)\)-optimal |
| 164934.w2 | 164934dg2 | \([1, -1, 0, -82917, 11001199]\) | \(-735091890625/181908738\) | \(-15601606834265298\) | \([2]\) | \(1474560\) | \(1.8253\) |
Rank
sage: E.rank()
The elliptic curves in class 164934dg have rank \(1\).
Complex multiplication
The elliptic curves in class 164934dg do not have complex multiplication.Modular form 164934.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
