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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 132300.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 132300.c1 | 132300bb1 | \([0, 0, 0, -793800, -273199500]\) | \(-5971968/25\) | \(-231568526700000000\) | \([]\) | \(1959552\) | \(2.1869\) | \(\Gamma_0(N)\)-optimal |
| 132300.c2 | 132300bb2 | \([0, 0, 0, 1852200, -1440085500]\) | \(8429568/15625\) | \(-1302572962687500000000\) | \([]\) | \(5878656\) | \(2.7362\) |
Rank
sage: E.rank()
The elliptic curves in class 132300.c have rank \(0\).
Complex multiplication
The elliptic curves in class 132300.c do not have complex multiplication.Modular form 132300.2.a.c
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
