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SageMath
E = EllipticCurve("ed1")
E.isogeny_class()
Elliptic curves in class 190575.ed
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 190575.ed1 | 190575dc2 | \([1, -1, 0, -19820367, 33954943666]\) | \(341385539669/160083\) | \(403793099377787109375\) | \([2]\) | \(9216000\) | \(2.9098\) | |
| 190575.ed2 | 190575dc1 | \([1, -1, 0, -1443492, 343639291]\) | \(131872229/56133\) | \(141589788093509765625\) | \([2]\) | \(4608000\) | \(2.5632\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 190575.ed have rank \(1\).
Complex multiplication
The elliptic curves in class 190575.ed do not have complex multiplication.Modular form 190575.2.a.ed
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.
