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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 185900.w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 185900.w1 | 185900w1 | \([0, 0, 0, -13000, -570375]\) | \(442368000/121\) | \(66459250000\) | \([2]\) | \(259200\) | \(1.0593\) | \(\Gamma_0(N)\)-optimal |
| 185900.w2 | 185900w2 | \([0, 0, 0, -11375, -718250]\) | \(-18522000/14641\) | \(-128665108000000\) | \([2]\) | \(518400\) | \(1.4059\) |
Rank
sage: E.rank()
The elliptic curves in class 185900.w have rank \(0\).
Complex multiplication
The elliptic curves in class 185900.w do not have complex multiplication.Modular form 185900.2.a.w
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
