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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 326700.x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 326700.x1 | 326700x1 | \([0, 0, 0, -6724575, -6711900250]\) | \(-175767417072/55\) | \(-10523072340000000\) | \([]\) | \(9953280\) | \(2.4363\) | \(\Gamma_0(N)\)-optimal |
| 326700.x2 | 326700x2 | \([0, 0, 0, -5635575, -8957297250]\) | \(-141915888/166375\) | \(-23205742200976500000000\) | \([]\) | \(29859840\) | \(2.9856\) |
Rank
sage: E.rank()
The elliptic curves in class 326700.x have rank \(0\).
Complex multiplication
The elliptic curves in class 326700.x do not have complex multiplication.Modular form 326700.2.a.x
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.
