Show commands:
SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 435120.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
435120.d1 | 435120d2 | \([0, -1, 0, -715416, -232251984]\) | \(84033427451401/174650175\) | \(84162225924403200\) | \([2]\) | \(7077888\) | \(2.1333\) | \(\Gamma_0(N)\)-optimal* |
435120.d2 | 435120d1 | \([0, -1, 0, -29416, -6146384]\) | \(-5841725401/30594375\) | \(-14743132669440000\) | \([2]\) | \(3538944\) | \(1.7867\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 435120.d have rank \(1\).
Complex multiplication
The elliptic curves in class 435120.d do not have complex multiplication.Modular form 435120.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.