Show commands:
SageMath
E = EllipticCurve("eb1")
E.isogeny_class()
Elliptic curves in class 78400.eb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
78400.eb1 | 78400bq3 | \([0, -1, 0, -643533, 208075687]\) | \(-250523582464/13671875\) | \(-1608482421875000000\) | \([]\) | \(995328\) | \(2.2517\) | |
78400.eb2 | 78400bq1 | \([0, -1, 0, -6533, -223313]\) | \(-262144/35\) | \(-4117715000000\) | \([]\) | \(110592\) | \(1.1531\) | \(\Gamma_0(N)\)-optimal |
78400.eb3 | 78400bq2 | \([0, -1, 0, 42467, 560687]\) | \(71991296/42875\) | \(-5044200875000000\) | \([]\) | \(331776\) | \(1.7024\) |
Rank
sage: E.rank()
The elliptic curves in class 78400.eb have rank \(0\).
Complex multiplication
The elliptic curves in class 78400.eb do not have complex multiplication.Modular form 78400.2.a.eb
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.
\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.