Show commands:
SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 6300.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6300.d1 | 6300h2 | \([0, 0, 0, -181200, 29688500]\) | \(-225637236736/1715\) | \(-5000940000000\) | \([]\) | \(25920\) | \(1.6116\) | |
6300.d2 | 6300h1 | \([0, 0, 0, -1200, 78500]\) | \(-65536/875\) | \(-2551500000000\) | \([]\) | \(8640\) | \(1.0623\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 6300.d have rank \(1\).
Complex multiplication
The elliptic curves in class 6300.d do not have complex multiplication.Modular form 6300.2.a.d
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.