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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 8820.t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 8820.t1 | 8820z2 | \([0, 0, 0, -210567, 37189726]\) | \(16129950234928/455625\) | \(29165482080000\) | \([2]\) | \(36864\) | \(1.6855\) | |
| 8820.t2 | 8820z1 | \([0, 0, 0, -13692, 531601]\) | \(70954958848/10546875\) | \(42195431250000\) | \([2]\) | \(18432\) | \(1.3390\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 8820.t have rank \(1\).
Complex multiplication
The elliptic curves in class 8820.t do not have complex multiplication.Modular form 8820.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
