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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 11270f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11270.f2 | 11270f1 | \([1, -1, 0, -43619, 4767125]\) | \(-78013216986489/37918720000\) | \(-4461099489280000\) | \([2]\) | \(64512\) | \(1.7083\) | \(\Gamma_0(N)\)-optimal |
| 11270.f1 | 11270f2 | \([1, -1, 0, -764899, 257647893]\) | \(420676324562824569/56350000000\) | \(6629521150000000\) | \([2]\) | \(129024\) | \(2.0549\) |
Rank
sage: E.rank()
The elliptic curves in class 11270f have rank \(1\).
Complex multiplication
The elliptic curves in class 11270f do not have complex multiplication.Modular form 11270.2.a.f
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 Cremona 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 Cremona labels.
