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SageMath
E = EllipticCurve("gv1")
E.isogeny_class()
Elliptic curves in class 270480.gv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 270480.gv1 | 270480gv6 | \([0, 1, 0, -69685856, -223928874156]\) | \(155324313723954725282/13018359375\) | \(3136710578400000000\) | \([2]\) | \(22020096\) | \(2.9916\) | |
| 270480.gv2 | 270480gv3 | \([0, 1, 0, -5997616, 5645498564]\) | \(198048499826486404/242568272835\) | \(29222824684303272960\) | \([2]\) | \(11010048\) | \(2.6450\) | |
| 270480.gv3 | 270480gv4 | \([0, 1, 0, -4364936, -3483833340]\) | \(76343005935514084/694180580625\) | \(83629722757069440000\) | \([2, 2]\) | \(11010048\) | \(2.6450\) | |
| 270480.gv4 | 270480gv5 | \([0, 1, 0, -1277936, -8313136140]\) | \(-957928673903042/123339801817575\) | \(-29718127296585484646400\) | \([2]\) | \(22020096\) | \(2.9916\) | |
| 270480.gv5 | 270480gv2 | \([0, 1, 0, -475316, 37050684]\) | \(394315384276816/208332909225\) | \(6274600559977478400\) | \([2, 2]\) | \(5505024\) | \(2.2985\) | |
| 270480.gv6 | 270480gv1 | \([0, 1, 0, 112929, 4579560]\) | \(84611246065664/53699121315\) | \(-101082366777414960\) | \([2]\) | \(2752512\) | \(1.9519\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 270480.gv have rank \(0\).
Complex multiplication
The elliptic curves in class 270480.gv do not have complex multiplication.Modular form 270480.2.a.gv
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.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 4 & 8 \\ 8 & 1 & 4 & 8 & 2 & 4 \\ 2 & 4 & 1 & 2 & 2 & 4 \\ 4 & 8 & 2 & 1 & 4 & 8 \\ 4 & 2 & 2 & 4 & 1 & 2 \\ 8 & 4 & 4 & 8 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
