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SageMath
E = EllipticCurve("bv1")
E.isogeny_class()
Elliptic curves in class 73920.bv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 73920.bv1 | 73920ew6 | \([0, -1, 0, -848001, 300836385]\) | \(257260669489908001/14267882475\) | \(3740239783526400\) | \([2]\) | \(1048576\) | \(2.0536\) | |
| 73920.bv2 | 73920ew4 | \([0, -1, 0, -56001, 4153185]\) | \(74093292126001/14707625625\) | \(3855515811840000\) | \([2, 2]\) | \(524288\) | \(1.7070\) | |
| 73920.bv3 | 73920ew2 | \([0, -1, 0, -17281, -810719]\) | \(2177286259681/161417025\) | \(42314504601600\) | \([2, 2]\) | \(262144\) | \(1.3604\) | |
| 73920.bv4 | 73920ew1 | \([0, -1, 0, -16961, -844575]\) | \(2058561081361/12705\) | \(3330539520\) | \([2]\) | \(131072\) | \(1.0139\) | \(\Gamma_0(N)\)-optimal |
| 73920.bv5 | 73920ew3 | \([0, -1, 0, 16319, -3612959]\) | \(1833318007919/22507682505\) | \(-5900253922590720\) | \([2]\) | \(524288\) | \(1.7070\) | |
| 73920.bv6 | 73920ew5 | \([0, -1, 0, 116479, 24540321]\) | \(666688497209279/1381398046875\) | \(-362125209600000000\) | \([2]\) | \(1048576\) | \(2.0536\) |
Rank
sage: E.rank()
The elliptic curves in class 73920.bv have rank \(2\).
Complex multiplication
The elliptic curves in class 73920.bv do not have complex multiplication.Modular form 73920.2.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 LMFDB numbering.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 8 & 4 \\ 2 & 1 & 2 & 4 & 4 & 2 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 2 & 4 & 8 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
