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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 193200.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 193200.m1 | 193200em2 | \([0, -1, 0, -1338608, -520308288]\) | \(4144806984356137/568114785504\) | \(36359346272256000000\) | \([2]\) | \(5898240\) | \(2.4802\) | |
| 193200.m2 | 193200em1 | \([0, -1, 0, 133392, -43380288]\) | \(4101378352343/15049939968\) | \(-963196157952000000\) | \([2]\) | \(2949120\) | \(2.1336\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 193200.m have rank \(0\).
Complex multiplication
The elliptic curves in class 193200.m do not have complex multiplication.Modular form 193200.2.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.
