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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 185900l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 185900.i2 | 185900l1 | \([0, -1, 0, 383067, -41667263]\) | \(321978368/224939\) | \(-4342950358604000000\) | \([]\) | \(2177280\) | \(2.2648\) | \(\Gamma_0(N)\)-optimal |
| 185900.i1 | 185900l2 | \([0, -1, 0, -7052933, -7369845263]\) | \(-2009615368192/53094899\) | \(-1025115745389164000000\) | \([]\) | \(6531840\) | \(2.8141\) |
Rank
sage: E.rank()
The elliptic curves in class 185900l have rank \(0\).
Complex multiplication
The elliptic curves in class 185900l do not have complex multiplication.Modular form 185900.2.a.l
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.
