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SageMath
E = EllipticCurve("bz1")
E.isogeny_class()
Elliptic curves in class 32400bz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 32400.f2 | 32400bz1 | \([0, 0, 0, 1725, -2750]\) | \(109503/64\) | \(-331776000000\) | \([]\) | \(31104\) | \(0.90006\) | \(\Gamma_0(N)\)-optimal |
| 32400.f1 | 32400bz2 | \([0, 0, 0, -22275, 1397250]\) | \(-35937/4\) | \(-136048896000000\) | \([]\) | \(93312\) | \(1.4494\) |
Rank
sage: E.rank()
The elliptic curves in class 32400bz have rank \(0\).
Complex multiplication
The elliptic curves in class 32400bz do not have complex multiplication.Modular form 32400.2.a.bz
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
