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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 168948ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 168948.bh2 | 168948ba1 | \([0, 0, 0, -17328, 788785]\) | \(1048576/117\) | \(64202949250128\) | \([2]\) | \(684288\) | \(1.3824\) | \(\Gamma_0(N)\)-optimal |
| 168948.bh1 | 168948ba2 | \([0, 0, 0, -66063, -5692970]\) | \(3631696/507\) | \(4451404481342208\) | \([2]\) | \(1368576\) | \(1.7290\) |
Rank
sage: E.rank()
The elliptic curves in class 168948ba have rank \(0\).
Complex multiplication
The elliptic curves in class 168948ba do not have complex multiplication.Modular form 168948.2.a.ba
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.
