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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 103056t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 103056.n2 | 103056t1 | \([0, -1, 0, -66552, -6476688]\) | \(7958910549046393/151342682688\) | \(619899628290048\) | \([2]\) | \(497664\) | \(1.6318\) | \(\Gamma_0(N)\)-optimal |
| 103056.n1 | 103056t2 | \([0, -1, 0, -138872, 10185840]\) | \(72312097990757113/31003988313096\) | \(126992336130441216\) | \([2]\) | \(995328\) | \(1.9784\) |
Rank
sage: E.rank()
The elliptic curves in class 103056t have rank \(0\).
Complex multiplication
The elliptic curves in class 103056t do not have complex multiplication.Modular form 103056.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
