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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 152460br
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 152460.p1 | 152460br1 | \([0, 0, 0, -4158528, -3264055223]\) | \(10392086293512192/1684375\) | \(1289076361650000\) | \([2]\) | \(2995200\) | \(2.3013\) | \(\Gamma_0(N)\)-optimal |
| 152460.p2 | 152460br2 | \([0, 0, 0, -4145823, -3284990522]\) | \(-643570518871152/8271484375\) | \(-101284571272500000000\) | \([2]\) | \(5990400\) | \(2.6479\) |
Rank
sage: E.rank()
The elliptic curves in class 152460br have rank \(0\).
Complex multiplication
The elliptic curves in class 152460br do not have complex multiplication.Modular form 152460.2.a.br
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.
