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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 18928q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
18928.y1 | 18928q1 | \([0, -1, 0, -10872, -432784]\) | \(-1214950633/196\) | \(-22929227776\) | \([]\) | \(34560\) | \(0.99745\) | \(\Gamma_0(N)\)-optimal |
18928.y2 | 18928q2 | \([0, -1, 0, 2648, -1427856]\) | \(17546087/7529536\) | \(-880849214242816\) | \([]\) | \(103680\) | \(1.5468\) |
Rank
sage: E.rank()
The elliptic curves in class 18928q have rank \(0\).
Complex multiplication
The elliptic curves in class 18928q do not have complex multiplication.Modular form 18928.2.a.q
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.