Show commands:
SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 30576.w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
30576.w1 | 30576h1 | \([0, -1, 0, -163, -314]\) | \(256000/117\) | \(220238928\) | \([2]\) | \(9216\) | \(0.29578\) | \(\Gamma_0(N)\)-optimal |
30576.w2 | 30576h2 | \([0, -1, 0, 572, -2960]\) | \(686000/507\) | \(-15269899008\) | \([2]\) | \(18432\) | \(0.64235\) |
Rank
sage: E.rank()
The elliptic curves in class 30576.w have rank \(1\).
Complex multiplication
The elliptic curves in class 30576.w do not have complex multiplication.Modular form 30576.2.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.