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SageMath
E = EllipticCurve("dg1")
E.isogeny_class()
Elliptic curves in class 194922dg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 194922.bb2 | 194922dg1 | \([1, -1, 0, -981805365, -13677875641571]\) | \(-24905087205614147556241/4819348696095929736\) | \(-20253505327117231129918428744\) | \([]\) | \(116960256\) | \(4.1550\) | \(\Gamma_0(N)\)-optimal |
| 194922.bb1 | 194922dg2 | \([1, -1, 0, -38664413055, 3915352734580237]\) | \(-1521059241134755603512440881/695595284594977727840256\) | \(-2923266957934512494114370773581824\) | \([]\) | \(818721792\) | \(5.1280\) |
Rank
sage: E.rank()
The elliptic curves in class 194922dg have rank \(0\).
Complex multiplication
The elliptic curves in class 194922dg do not have complex multiplication.Modular form 194922.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
