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SageMath
E = EllipticCurve("dg1")
E.isogeny_class()
Elliptic curves in class 121968.dg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 121968.dg1 | 121968da2 | \([0, 0, 0, -452626515, -3706478284014]\) | \(-4904170882875/43904\) | \(-91808349892676770332672\) | \([]\) | \(22353408\) | \(3.5718\) | |
| 121968.dg2 | 121968da1 | \([0, 0, 0, -2854995, -10046039278]\) | \(-897199875/14680064\) | \(-42109347572621600882688\) | \([]\) | \(7451136\) | \(3.0225\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 121968.dg have rank \(0\).
Complex multiplication
The elliptic curves in class 121968.dg do not have complex multiplication.Modular form 121968.2.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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
