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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 185900e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 185900.c2 | 185900e1 | \([0, 1, 0, -22533, 63688]\) | \(1048576/605\) | \(730054861250000\) | \([2]\) | \(677376\) | \(1.5415\) | \(\Gamma_0(N)\)-optimal |
| 185900.c1 | 185900e2 | \([0, 1, 0, -254908, 49327188]\) | \(94875856/275\) | \(5309489900000000\) | \([2]\) | \(1354752\) | \(1.8881\) |
Rank
sage: E.rank()
The elliptic curves in class 185900e have rank \(0\).
Complex multiplication
The elliptic curves in class 185900e do not have complex multiplication.Modular form 185900.2.a.e
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.
