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SageMath
E = EllipticCurve("jm1")
E.isogeny_class()
Elliptic curves in class 176400jm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 176400.cs2 | 176400jm1 | \([0, 0, 0, -132300, -10418625]\) | \(442368/175\) | \(101311230431250000\) | \([2]\) | \(1327104\) | \(1.9615\) | \(\Gamma_0(N)\)-optimal |
| 176400.cs1 | 176400jm2 | \([0, 0, 0, -959175, 354233250]\) | \(10536048/245\) | \(2269371561660000000\) | \([2]\) | \(2654208\) | \(2.3081\) |
Rank
sage: E.rank()
The elliptic curves in class 176400jm have rank \(1\).
Complex multiplication
The elliptic curves in class 176400jm do not have complex multiplication.Modular form 176400.2.a.jm
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 Cremona 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 Cremona labels.
