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SageMath
E = EllipticCurve("fz1")
E.isogeny_class()
Elliptic curves in class 148800.fz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 148800.fz1 | 148800ha2 | \([0, 1, 0, -349516033, 2514945908063]\) | \(1152829477932246539641/3188367360\) | \(13059552706560000000\) | \([2]\) | \(19169280\) | \(3.3262\) | |
| 148800.fz2 | 148800ha1 | \([0, 1, 0, -21836033, 39323508063]\) | \(-281115640967896441/468084326400\) | \(-1917273400934400000000\) | \([2]\) | \(9584640\) | \(2.9796\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 148800.fz have rank \(1\).
Complex multiplication
The elliptic curves in class 148800.fz do not have complex multiplication.Modular form 148800.2.a.fz
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.
