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SageMath
E = EllipticCurve("ff1")
E.isogeny_class()
Elliptic curves in class 705600.ff
sage: E.isogeny_class().curves
| LMFDB label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height |
|---|---|---|---|---|---|---|
| 705600.ff1 | \([0, 0, 0, -13891500, -19911150000]\) | \(1000188\) | \(296407714176000000000\) | \([2]\) | \(35389440\) | \(2.8476\) |
| 705600.ff2 | \([0, 0, 0, -661500, -463050000]\) | \(-432\) | \(-74101928544000000000\) | \([2]\) | \(17694720\) | \(2.5010\) |
Rank
sage: E.rank()
The elliptic curves in class 705600.ff have rank \(0\).
Complex multiplication
The elliptic curves in class 705600.ff do not have complex multiplication.Modular form 705600.2.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 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.
