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SageMath
E = EllipticCurve("dg1")
E.isogeny_class()
Elliptic curves in class 116928dg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 116928.ci2 | 116928dg1 | \([0, 0, 0, -76620, 9667856]\) | \(-1041220466500/242597383\) | \(-11590270465277952\) | \([2]\) | \(589824\) | \(1.8018\) | \(\Gamma_0(N)\)-optimal |
| 116928.ci1 | 116928dg2 | \([0, 0, 0, -1287660, 562386512]\) | \(2471097448795250/98942809\) | \(9454132626849792\) | \([2]\) | \(1179648\) | \(2.1484\) |
Rank
sage: E.rank()
The elliptic curves in class 116928dg have rank \(1\).
Complex multiplication
The elliptic curves in class 116928dg do not have complex multiplication.Modular form 116928.2.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.
