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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 88445.x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 88445.x1 | 88445d1 | \([0, -1, 1, -4870371, -4135466924]\) | \(-47109013504/475\) | \(-128824817371473475\) | \([]\) | \(2177280\) | \(2.4420\) | \(\Gamma_0(N)\)-optimal |
| 88445.x2 | 88445d2 | \([0, -1, 1, -2393911, -8324770483]\) | \(-5594251264/107171875\) | \(-29066099419438702796875\) | \([]\) | \(6531840\) | \(2.9913\) |
Rank
sage: E.rank()
The elliptic curves in class 88445.x have rank \(0\).
Complex multiplication
The elliptic curves in class 88445.x do not have complex multiplication.Modular form 88445.2.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.
