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SageMath
E = EllipticCurve("iz1")
E.isogeny_class()
Elliptic curves in class 296450iz
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
296450.iz1 | 296450iz1 | \([1, 0, 0, -63146938, 193536262492]\) | \(-584043889/1400\) | \(-66751826463066696875000\) | \([]\) | \(43794432\) | \(3.2590\) | \(\Gamma_0(N)\)-optimal |
296450.iz2 | 296450iz2 | \([1, 0, 0, 116205312, 974974015742]\) | \(3639707951/10718750\) | \(-511068671357854397949218750\) | \([]\) | \(131383296\) | \(3.8083\) |
Rank
sage: E.rank()
The elliptic curves in class 296450iz have rank \(0\).
Complex multiplication
The elliptic curves in class 296450iz do not have complex multiplication.Modular form 296450.2.a.iz
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.