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SageMath
E = EllipticCurve("ea1")
E.isogeny_class()
Elliptic curves in class 145200.ea
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
145200.ea1 | 145200ks1 | \([0, -1, 0, -33067283, -73177962438]\) | \(9028656748079104/3969405\) | \(1758010772801250000\) | \([2]\) | \(8847360\) | \(2.8423\) | \(\Gamma_0(N)\)-optimal |
145200.ea2 | 145200ks2 | \([0, -1, 0, -32900908, -73950940688]\) | \(-555816294307024/11837848275\) | \(-83885881311629100000000\) | \([2]\) | \(17694720\) | \(3.1889\) |
Rank
sage: E.rank()
The elliptic curves in class 145200.ea have rank \(0\).
Complex multiplication
The elliptic curves in class 145200.ea do not have complex multiplication.Modular form 145200.2.a.ea
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.