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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 50960.ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 50960.ba1 | 50960d1 | \([0, 0, 0, -134603, -941878]\) | \(2238719766084/1292374265\) | \(155695656860656640\) | \([2]\) | \(331776\) | \(1.9884\) | \(\Gamma_0(N)\)-optimal |
| 50960.ba2 | 50960d2 | \([0, 0, 0, 537677, -7530222]\) | \(71346044015118/41389887175\) | \(-9972692656643225600\) | \([2]\) | \(663552\) | \(2.3350\) |
Rank
sage: E.rank()
The elliptic curves in class 50960.ba have rank \(1\).
Complex multiplication
The elliptic curves in class 50960.ba do not have complex multiplication.Modular form 50960.2.a.ba
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.
