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SageMath
E = EllipticCurve("rz1")
E.isogeny_class()
Elliptic curves in class 176400.rz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 176400.rz1 | 176400ks2 | \([0, 0, 0, -106575, -13119750]\) | \(10536048/245\) | \(3112992540000000\) | \([2]\) | \(884736\) | \(1.7587\) | |
| 176400.rz2 | 176400ks1 | \([0, 0, 0, -14700, 385875]\) | \(442368/175\) | \(138972881250000\) | \([2]\) | \(442368\) | \(1.4122\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 176400.rz have rank \(1\).
Complex multiplication
The elliptic curves in class 176400.rz do not have complex multiplication.Modular form 176400.2.a.rz
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.
