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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 56784.t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 56784.t1 | 56784bd2 | \([0, -1, 0, -27305048, 53541730800]\) | \(673822943613625/19421724672\) | \(64892508036112582705152\) | \([]\) | \(5660928\) | \(3.1553\) | |
| 56784.t2 | 56784bd1 | \([0, -1, 0, -3577448, -2576890512]\) | \(1515434103625/17635968\) | \(58925878854340313088\) | \([]\) | \(1886976\) | \(2.6060\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 56784.t have rank \(0\).
Complex multiplication
The elliptic curves in class 56784.t do not have complex multiplication.Modular form 56784.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
