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SageMath
E = EllipticCurve("hb1")
E.isogeny_class()
Elliptic curves in class 388080.hb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 388080.hb1 | 388080hb2 | \([0, 0, 0, -33663, -2357782]\) | \(192143824/1815\) | \(39850370461440\) | \([2]\) | \(1179648\) | \(1.4304\) | |
| 388080.hb2 | 388080hb1 | \([0, 0, 0, -588, -88837]\) | \(-16384/2475\) | \(-3396338391600\) | \([2]\) | \(589824\) | \(1.0839\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 388080.hb have rank \(1\).
Complex multiplication
The elliptic curves in class 388080.hb do not have complex multiplication.Modular form 388080.2.a.hb
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.
