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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 227430.a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 227430.a1 | 227430ex1 | \([1, -1, 0, -5695537680, 165445113797100]\) | \(595770186172725915913801/16492385700\) | \(565630236170211939300\) | \([2]\) | \(141926400\) | \(3.9441\) | \(\Gamma_0(N)\)-optimal |
| 227430.a2 | 227430ex2 | \([1, -1, 0, -5695310250, 165458987072586]\) | \(-595698819458679957260521/99124922039928750\) | \(-3399632659803653846093508750\) | \([2]\) | \(283852800\) | \(4.2907\) |
Rank
sage: E.rank()
The elliptic curves in class 227430.a have rank \(1\).
Complex multiplication
The elliptic curves in class 227430.a do not have complex multiplication.Modular form 227430.2.a.a
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.
