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SageMath
E = EllipticCurve("ff1")
E.isogeny_class()
Elliptic curves in class 149184ff
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
149184.dl1 | 149184ff1 | \([0, 0, 0, -360, -1944]\) | \(6912000/1813\) | \(1353397248\) | \([2]\) | \(57344\) | \(0.46097\) | \(\Gamma_0(N)\)-optimal |
149184.dl2 | 149184ff2 | \([0, 0, 0, 900, -12528]\) | \(6750000/9583\) | \(-114458738688\) | \([2]\) | \(114688\) | \(0.80754\) |
Rank
sage: E.rank()
The elliptic curves in class 149184ff have rank \(1\).
Complex multiplication
The elliptic curves in class 149184ff do not have complex multiplication.Modular form 149184.2.a.ff
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.