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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 53130.t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 53130.t1 | 53130s4 | \([1, 0, 1, -24314, -1461238]\) | \(1589524669089018649/6833846250\) | \(6833846250\) | \([2]\) | \(106496\) | \(1.0944\) | |
| 53130.t2 | 53130s3 | \([1, 0, 1, -4694, 96266]\) | \(11434573275812569/2581205811030\) | \(2581205811030\) | \([2]\) | \(106496\) | \(1.0944\) | |
| 53130.t3 | 53130s2 | \([1, 0, 1, -1544, -22174]\) | \(406687851166969/25405172100\) | \(25405172100\) | \([2, 2]\) | \(53248\) | \(0.74784\) | |
| 53130.t4 | 53130s1 | \([1, 0, 1, 76, -1438]\) | \(49471280711/929562480\) | \(-929562480\) | \([2]\) | \(26624\) | \(0.40127\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 53130.t have rank \(1\).
Complex multiplication
The elliptic curves in class 53130.t do not have complex multiplication.Modular form 53130.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
