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SageMath
E = EllipticCurve("ew1")
E.isogeny_class()
Elliptic curves in class 101430ew
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
101430.eq2 | 101430ew1 | \([1, -1, 1, -84902, -9311151]\) | \(789145184521/17996580\) | \(1543496857866180\) | \([2]\) | \(737280\) | \(1.7010\) | \(\Gamma_0(N)\)-optimal |
101430.eq1 | 101430ew2 | \([1, -1, 1, -186332, 17304081]\) | \(8341959848041/3327411150\) | \(285379147307649150\) | \([2]\) | \(1474560\) | \(2.0476\) |
Rank
sage: E.rank()
The elliptic curves in class 101430ew have rank \(1\).
Complex multiplication
The elliptic curves in class 101430ew do not have complex multiplication.Modular form 101430.2.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.