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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 69300.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 69300.c1 | 69300c1 | \([0, 0, 0, -1725, 28625]\) | \(-84098304/3773\) | \(-25467750000\) | \([]\) | \(62208\) | \(0.76122\) | \(\Gamma_0(N)\)-optimal |
| 69300.c2 | 69300c2 | \([0, 0, 0, 8775, 77625]\) | \(15185664/9317\) | \(-45846627750000\) | \([]\) | \(186624\) | \(1.3105\) |
Rank
sage: E.rank()
The elliptic curves in class 69300.c have rank \(0\).
Complex multiplication
The elliptic curves in class 69300.c do not have complex multiplication.Modular form 69300.2.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.
