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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 54150.j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 54150.j1 | 54150f2 | \([1, 1, 0, -3587625, -2613540375]\) | \(6947097508441/10687500\) | \(7856294581054687500\) | \([2]\) | \(1658880\) | \(2.5250\) | |
| 54150.j2 | 54150f1 | \([1, 1, 0, -158125, -65421875]\) | \(-594823321/2166000\) | \(-1592209035093750000\) | \([2]\) | \(829440\) | \(2.1784\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 54150.j have rank \(0\).
Complex multiplication
The elliptic curves in class 54150.j do not have complex multiplication.Modular form 54150.2.a.j
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.
