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SageMath
E = EllipticCurve("hb1")
E.isogeny_class()
Elliptic curves in class 166464.hb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 166464.hb1 | 166464gi2 | \([0, 0, 0, -74951436, 249757219312]\) | \(-843137281012581793/216\) | \(-11929412173824\) | \([]\) | \(10450944\) | \(2.7916\) | |
| 166464.hb2 | 166464gi1 | \([0, 0, 0, -923916, 343698928]\) | \(-1579268174113/10077696\) | \(-556578654381932544\) | \([]\) | \(3483648\) | \(2.2423\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 166464.hb have rank \(0\).
Complex multiplication
The elliptic curves in class 166464.hb do not have complex multiplication.Modular form 166464.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
