Show commands:
SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 3465.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3465.b1 | 3465k3 | \([1, -1, 1, -186323, 8817072]\) | \(981281029968144361/522287841796875\) | \(380747836669921875\) | \([2]\) | \(36864\) | \(2.0648\) | |
| 3465.b2 | 3465k2 | \([1, -1, 1, -146228, 21535206]\) | \(474334834335054841/607815140625\) | \(443097237515625\) | \([2, 2]\) | \(18432\) | \(1.7182\) | |
| 3465.b3 | 3465k1 | \([1, -1, 1, -146183, 21549102]\) | \(473897054735271721/779625\) | \(568346625\) | \([2]\) | \(9216\) | \(1.3716\) | \(\Gamma_0(N)\)-optimal |
| 3465.b4 | 3465k4 | \([1, -1, 1, -106853, 33363456]\) | \(-185077034913624841/551466161890875\) | \(-402018832018447875\) | \([2]\) | \(36864\) | \(2.0648\) |
Rank
sage: E.rank()
The elliptic curves in class 3465.b have rank \(0\).
Complex multiplication
The elliptic curves in class 3465.b do not have complex multiplication.Modular form 3465.2.a.b
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
