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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 11025.w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11025.w1 | 11025q2 | \([0, 0, 1, -2263800, 1313722156]\) | \(-19539165184/46875\) | \(-3078032174560546875\) | \([]\) | \(193536\) | \(2.4269\) | |
| 11025.w2 | 11025q1 | \([0, 0, 1, 51450, 9078781]\) | \(229376/675\) | \(-44323663313671875\) | \([]\) | \(64512\) | \(1.8776\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 11025.w have rank \(0\).
Complex multiplication
The elliptic curves in class 11025.w do not have complex multiplication.Modular form 11025.2.a.w
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.
