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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 134640bj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 134640.fa2 | 134640bj1 | \([0, 0, 0, -3281547, -12542060486]\) | \(-1308796492121439049/22000592486400000\) | \(-65693417154910617600000\) | \([2]\) | \(9584640\) | \(3.0595\) | \(\Gamma_0(N)\)-optimal |
| 134640.fa1 | 134640bj2 | \([0, 0, 0, -103551627, -404056614854]\) | \(41125104693338423360329/179205840000000000\) | \(535105770946560000000000\) | \([2]\) | \(19169280\) | \(3.4061\) |
Rank
sage: E.rank()
The elliptic curves in class 134640bj have rank \(0\).
Complex multiplication
The elliptic curves in class 134640bj do not have complex multiplication.Modular form 134640.2.a.bj
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.
