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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 111090.t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 111090.t1 | 111090q3 | \([1, 0, 1, -1527499, 238846262]\) | \(2662558086295801/1374177967680\) | \(203427657089722067520\) | \([2]\) | \(4561920\) | \(2.5889\) | |
| 111090.t2 | 111090q1 | \([1, 0, 1, -853024, -303304678]\) | \(463702796512201/15214500\) | \(2252292033190500\) | \([2]\) | \(1520640\) | \(2.0396\) | \(\Gamma_0(N)\)-optimal |
| 111090.t3 | 111090q2 | \([1, 0, 1, -815994, -330825374]\) | \(-405897921250921/84358968750\) | \(-12488154934029468750\) | \([2]\) | \(3041280\) | \(2.3862\) | |
| 111090.t4 | 111090q4 | \([1, 0, 1, 5730381, 1855901926]\) | \(140574743422291079/91397357868600\) | \(-13530089124329346185400\) | \([2]\) | \(9123840\) | \(2.9355\) |
Rank
sage: E.rank()
The elliptic curves in class 111090.t have rank \(1\).
Complex multiplication
The elliptic curves in class 111090.t do not have complex multiplication.Modular form 111090.2.a.t
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
