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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 144400.br
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 144400.br1 | 144400u2 | \([0, 0, 0, -3564875, 2529256250]\) | \(13312053/361\) | \(135868504328000000000\) | \([2]\) | \(3686400\) | \(2.6434\) | |
| 144400.br2 | 144400u1 | \([0, 0, 0, 45125, 128606250]\) | \(27/19\) | \(-7150973912000000000\) | \([2]\) | \(1843200\) | \(2.2969\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 144400.br have rank \(0\).
Complex multiplication
The elliptic curves in class 144400.br do not have complex multiplication.Modular form 144400.2.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 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.
