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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 76050.ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 76050.ba1 | 76050i2 | \([1, -1, 0, -266967, 53129441]\) | \(1033364331/676\) | \(1376545591687500\) | \([2]\) | \(688128\) | \(1.8445\) | |
| 76050.ba2 | 76050i1 | \([1, -1, 0, -13467, 1161941]\) | \(-132651/208\) | \(-423552489750000\) | \([2]\) | \(344064\) | \(1.4980\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 76050.ba have rank \(1\).
Complex multiplication
The elliptic curves in class 76050.ba do not have complex multiplication.Modular form 76050.2.a.ba
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
