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SageMath
E = EllipticCurve("fc1")
E.isogeny_class()
Elliptic curves in class 388080fc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
388080.fc1 | 388080fc1 | \([0, 0, 0, -1641843, -748640718]\) | \(51603494067/4336640\) | \(41133233587334676480\) | \([2]\) | \(8847360\) | \(2.5054\) | \(\Gamma_0(N)\)-optimal |
388080.fc2 | 388080fc2 | \([0, 0, 0, 1745037, -3437146062]\) | \(61958108493/573927200\) | \(-5443726382573823590400\) | \([2]\) | \(17694720\) | \(2.8520\) |
Rank
sage: E.rank()
The elliptic curves in class 388080fc have rank \(0\).
Complex multiplication
The elliptic curves in class 388080fc do not have complex multiplication.Modular form 388080.2.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 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.