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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 54096.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 54096.m1 | 54096bo2 | \([0, -1, 0, -196207384, 1057855819504]\) | \(1733490909744055732873/99355964553216\) | \(47878675962762482417664\) | \([2]\) | \(9732096\) | \(3.4156\) | |
| 54096.m2 | 54096bo1 | \([0, -1, 0, -11559704, 18510958320]\) | \(-354499561600764553/101902222098432\) | \(-49105692785288914403328\) | \([2]\) | \(4866048\) | \(3.0690\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 54096.m have rank \(1\).
Complex multiplication
The elliptic curves in class 54096.m do not have complex multiplication.Modular form 54096.2.a.m
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.
