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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 8464.i
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 8464.i1 | 8464a2 | \([0, 0, 0, -18515, 754354]\) | \(2315250/529\) | \(160380897855488\) | \([2]\) | \(25344\) | \(1.4382\) | |
| 8464.i2 | 8464a1 | \([0, 0, 0, 2645, 73002]\) | \(13500/23\) | \(-3486541257728\) | \([2]\) | \(12672\) | \(1.0916\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 8464.i have rank \(0\).
Complex multiplication
The elliptic curves in class 8464.i do not have complex multiplication.Modular form 8464.2.a.i
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.
