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SageMath
E = EllipticCurve("ew1")
E.isogeny_class()
Elliptic curves in class 87120.ew
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 87120.ew1 | 87120bp2 | \([0, 0, 0, -1947, 32186]\) | \(821516/25\) | \(24839654400\) | \([2]\) | \(55296\) | \(0.77072\) | |
| 87120.ew2 | 87120bp1 | \([0, 0, 0, 33, 1694]\) | \(16/5\) | \(-1241982720\) | \([2]\) | \(27648\) | \(0.42414\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 87120.ew have rank \(1\).
Complex multiplication
The elliptic curves in class 87120.ew do not have complex multiplication.Modular form 87120.2.a.ew
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.
