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SageMath
E = EllipticCurve("dq1")
E.isogeny_class()
Elliptic curves in class 22050.dq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 22050.dq1 | 22050fn1 | \([1, -1, 1, -1929605, -1031210953]\) | \(-14822892630025/42\) | \(-2251360676250\) | \([]\) | \(230400\) | \(2.0268\) | \(\Gamma_0(N)\)-optimal |
| 22050.dq2 | 22050fn2 | \([1, -1, 1, 242320, -3183335053]\) | \(46969655/130691232\) | \(-4378468756777762500000\) | \([]\) | \(1152000\) | \(2.8315\) |
Rank
sage: E.rank()
The elliptic curves in class 22050.dq have rank \(1\).
Complex multiplication
The elliptic curves in class 22050.dq do not have complex multiplication.Modular form 22050.2.a.dq
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
