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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 185020c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 185020.b2 | 185020c1 | \([0, 1, 0, -25510, -1746975]\) | \(-162240822016/21484375\) | \(-243127843750000\) | \([3]\) | \(609120\) | \(1.4932\) | \(\Gamma_0(N)\)-optimal |
| 185020.b1 | 185020c2 | \([0, 1, 0, -2128010, -1195546475]\) | \(-94174415929782016/166375\) | \(-1882782022000\) | \([]\) | \(1827360\) | \(2.0425\) |
Rank
sage: E.rank()
The elliptic curves in class 185020c have rank \(0\).
Complex multiplication
The elliptic curves in class 185020c do not have complex multiplication.Modular form 185020.2.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 Cremona 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 Cremona labels.
