Show commands:
SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 63525.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 63525.l1 | 63525ba2 | \([1, 1, 1, -204553, -8243344]\) | \(4274401176989/2343775203\) | \(519017592800235375\) | \([2]\) | \(691200\) | \(2.0899\) | |
| 63525.l2 | 63525ba1 | \([1, 1, 1, -122878, 16422506]\) | \(926574216749/6792093\) | \(1504075883396625\) | \([2]\) | \(345600\) | \(1.7433\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 63525.l have rank \(1\).
Complex multiplication
The elliptic curves in class 63525.l do not have complex multiplication.Modular form 63525.2.a.l
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.
