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SageMath
E = EllipticCurve("bv1")
E.isogeny_class()
Elliptic curves in class 35904bv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 35904.l3 | 35904bv1 | \([0, -1, 0, -114449, -14864655]\) | \(10119139303540048/85833\) | \(1406287872\) | \([2]\) | \(98304\) | \(1.3416\) | \(\Gamma_0(N)\)-optimal |
| 35904.l2 | 35904bv2 | \([0, -1, 0, -114529, -14842751]\) | \(2535093488117092/7367303889\) | \(482823627669504\) | \([2, 2]\) | \(196608\) | \(1.6882\) | |
| 35904.l4 | 35904bv3 | \([0, -1, 0, -68289, -26985375]\) | \(-268702931670626/2248659199809\) | \(-294736258637365248\) | \([2]\) | \(393216\) | \(2.0348\) | |
| 35904.l1 | 35904bv4 | \([0, -1, 0, -162049, -1299551]\) | \(3590504967602306/2071799959977\) | \(271554964354105344\) | \([4]\) | \(393216\) | \(2.0348\) |
Rank
sage: E.rank()
The elliptic curves in class 35904bv have rank \(1\).
Complex multiplication
The elliptic curves in class 35904bv do not have complex multiplication.Modular form 35904.2.a.bv
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 Cremona 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 Cremona labels.
