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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 47025.z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 47025.z1 | 47025r1 | \([0, 0, 1, -6150, -217094]\) | \(-2258403328/480491\) | \(-5473092796875\) | \([]\) | \(77760\) | \(1.1656\) | \(\Gamma_0(N)\)-optimal |
| 47025.z2 | 47025r2 | \([0, 0, 1, 43350, 1255531]\) | \(790939860992/517504691\) | \(-5894701870921875\) | \([]\) | \(233280\) | \(1.7149\) |
Rank
sage: E.rank()
The elliptic curves in class 47025.z have rank \(1\).
Complex multiplication
The elliptic curves in class 47025.z do not have complex multiplication.Modular form 47025.2.a.z
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
