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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 253920t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 253920.t3 | 253920t1 | \([0, -1, 0, -16046, -748104]\) | \(48228544/2025\) | \(19185451214400\) | \([2, 2]\) | \(788480\) | \(1.3135\) | \(\Gamma_0(N)\)-optimal |
| 253920.t2 | 253920t2 | \([0, -1, 0, -42496, 2383576]\) | \(111980168/32805\) | \(2486434477386240\) | \([2]\) | \(1576960\) | \(1.6601\) | |
| 253920.t4 | 253920t3 | \([0, -1, 0, 7759, -2800095]\) | \(85184/5625\) | \(-3410746882560000\) | \([2]\) | \(1576960\) | \(1.6601\) | |
| 253920.t1 | 253920t4 | \([0, -1, 0, -254096, -49215084]\) | \(23937672968/45\) | \(3410746882560\) | \([2]\) | \(1576960\) | \(1.6601\) |
Rank
sage: E.rank()
The elliptic curves in class 253920t have rank \(1\).
Complex multiplication
The elliptic curves in class 253920t do not have complex multiplication.Modular form 253920.2.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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
