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SageMath
E = EllipticCurve("tm1")
E.isogeny_class()
Elliptic curves in class 176400.tm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 176400.tm1 | 176400jb2 | \([0, 0, 0, -3178875, -2180193750]\) | \(139798359/98\) | \(2490394032000000000\) | \([2]\) | \(4423680\) | \(2.4663\) | |
| 176400.tm2 | 176400jb1 | \([0, 0, 0, -238875, -19293750]\) | \(59319/28\) | \(711541152000000000\) | \([2]\) | \(2211840\) | \(2.1197\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 176400.tm have rank \(0\).
Complex multiplication
The elliptic curves in class 176400.tm do not have complex multiplication.Modular form 176400.2.a.tm
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.
