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SageMath
E = EllipticCurve("ff1")
E.isogeny_class()
Elliptic curves in class 242550.ff
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
242550.ff1 | 242550ff2 | \([1, -1, 0, -51608517, -142689138859]\) | \(144106117295241933/247808\) | \(26140913568000000\) | \([2]\) | \(15138816\) | \(2.8391\) | |
242550.ff2 | 242550ff1 | \([1, -1, 0, -3224517, -2230386859]\) | \(-35148950502093/46137344\) | \(-4866962817024000000\) | \([2]\) | \(7569408\) | \(2.4925\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 242550.ff have rank \(1\).
Complex multiplication
The elliptic curves in class 242550.ff do not have complex multiplication.Modular form 242550.2.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.