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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 28042a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 28042.c2 | 28042a1 | \([1, -1, 0, -1367381, 615777525]\) | \(-282743424546835350716073/117793097777152\) | \(-117793097777152\) | \([2]\) | \(236808\) | \(2.0446\) | \(\Gamma_0(N)\)-optimal |
| 28042.c1 | 28042a2 | \([1, -1, 0, -21878101, 39393344757]\) | \(1158117414329778748258778793/201005056\) | \(201005056\) | \([2]\) | \(473616\) | \(2.3912\) |
Rank
sage: E.rank()
The elliptic curves in class 28042a have rank \(1\).
Complex multiplication
The elliptic curves in class 28042a do not have complex multiplication.Modular form 28042.2.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 Cremona 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 Cremona labels.
