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SageMath
E = EllipticCurve("ew1")
E.isogeny_class()
Elliptic curves in class 92400ew
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 92400.l2 | 92400ew1 | \([0, -1, 0, -848, -4608]\) | \(131872229/56133\) | \(28740096000\) | \([2]\) | \(61440\) | \(0.70342\) | \(\Gamma_0(N)\)-optimal |
| 92400.l1 | 92400ew2 | \([0, -1, 0, -11648, -479808]\) | \(341385539669/160083\) | \(81962496000\) | \([2]\) | \(122880\) | \(1.0500\) |
Rank
sage: E.rank()
The elliptic curves in class 92400ew have rank \(1\).
Complex multiplication
The elliptic curves in class 92400ew do not have complex multiplication.Modular form 92400.2.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 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.
