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SageMath
E = EllipticCurve("er1")
E.isogeny_class()
Elliptic curves in class 123200.er
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 123200.er1 | 123200hl1 | \([0, 0, 0, -623500, 189450000]\) | \(52355598021/15092\) | \(7727104000000000\) | \([2]\) | \(1105920\) | \(2.0286\) | \(\Gamma_0(N)\)-optimal |
| 123200.er2 | 123200hl2 | \([0, 0, 0, -543500, 239850000]\) | \(-34677868581/28471058\) | \(-14577181696000000000\) | \([2]\) | \(2211840\) | \(2.3752\) |
Rank
sage: E.rank()
The elliptic curves in class 123200.er have rank \(0\).
Complex multiplication
The elliptic curves in class 123200.er do not have complex multiplication.Modular form 123200.2.a.er
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.
