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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 121275.a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 121275.a1 | 121275dp2 | \([0, 0, 1, -295363425, -36938069991594]\) | \(-2126464142970105856/438611057788643355\) | \(-587780766472480912668374296875\) | \([]\) | \(276480000\) | \(4.3915\) | |
| 121275.a2 | 121275dp1 | \([0, 0, 1, -98567175, 441097174656]\) | \(-79028701534867456/16987307596875\) | \(-22764616856528132373046875\) | \([]\) | \(55296000\) | \(3.5867\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 121275.a have rank \(1\).
Complex multiplication
The elliptic curves in class 121275.a do not have complex multiplication.Modular form 121275.2.a.a
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.
