Show commands:
SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 103056.w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
103056.w1 | 103056ba1 | \([0, 1, 0, -2104, -37804]\) | \(251598106297/412224\) | \(1688469504\) | \([2]\) | \(59904\) | \(0.66705\) | \(\Gamma_0(N)\)-optimal |
103056.w2 | 103056ba2 | \([0, 1, 0, -1464, -60588]\) | \(-84778086457/331891848\) | \(-1359429009408\) | \([2]\) | \(119808\) | \(1.0136\) |
Rank
sage: E.rank()
The elliptic curves in class 103056.w have rank \(2\).
Complex multiplication
The elliptic curves in class 103056.w do not have complex multiplication.Modular form 103056.2.a.w
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.