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SageMath
E = EllipticCurve("jo1")
E.isogeny_class()
Elliptic curves in class 176400.jo
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
176400.jo1 | 176400db2 | \([0, 0, 0, -1468233795, 21654139880450]\) | \(-162677523113838677\) | \(-2151700443648000\) | \([]\) | \(23869440\) | \(3.4859\) | |
176400.jo2 | 176400db1 | \([0, 0, 0, -56595, -5642350]\) | \(-9317\) | \(-2151700443648000\) | \([]\) | \(645120\) | \(1.6804\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 176400.jo have rank \(0\).
Complex multiplication
The elliptic curves in class 176400.jo do not have complex multiplication.Modular form 176400.2.a.jo
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.
\(\left(\begin{array}{rr} 1 & 37 \\ 37 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.