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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 72128.z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 72128.z1 | 72128bc2 | \([0, 0, 0, -746956, 247700880]\) | \(1494447319737/5411854\) | \(166906878032871424\) | \([2]\) | \(884736\) | \(2.1657\) | |
| 72128.z2 | 72128bc1 | \([0, 0, 0, -25676, 7370384]\) | \(-60698457/725788\) | \(-22384012797411328\) | \([2]\) | \(442368\) | \(1.8191\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 72128.z have rank \(1\).
Complex multiplication
The elliptic curves in class 72128.z do not have complex multiplication.Modular form 72128.2.a.z
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
