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SageMath
E = EllipticCurve("fc1")
E.isogeny_class()
Elliptic curves in class 227850.fc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
227850.fc1 | 227850dk2 | \([1, 1, 1, -45867088, -111556064719]\) | \(5805223604235668521/435937500000000\) | \(801368920898437500000000\) | \([2]\) | \(46448640\) | \(3.3321\) | |
227850.fc2 | 227850dk1 | \([1, 1, 1, 2740912, -7729376719]\) | \(1238798620042199/14760960000000\) | \(-27134565360000000000000\) | \([2]\) | \(23224320\) | \(2.9855\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 227850.fc have rank \(1\).
Complex multiplication
The elliptic curves in class 227850.fc do not have complex multiplication.Modular form 227850.2.a.fc
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.