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SageMath
E = EllipticCurve("ek1")
E.isogeny_class()
Elliptic curves in class 141120ek
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 141120.gn4 | 141120ek1 | \([0, 0, 0, -705668943, -7126549533992]\) | \(7079962908642659949376/100085966990454375\) | \(549375049939540209358680000\) | \([2]\) | \(82575360\) | \(3.9357\) | \(\Gamma_0(N)\)-optimal |
| 141120.gn2 | 141120ek2 | \([0, 0, 0, -11252115588, -459408804615488]\) | \(448487713888272974160064/91549016015625\) | \(32160989122670721600000000\) | \([2, 2]\) | \(165150720\) | \(4.2822\) | |
| 141120.gn3 | 141120ek3 | \([0, 0, 0, -11213536908, -462715414141232]\) | \(-55486311952875723077768/801237030029296875\) | \(-2251783932057135000000000000000\) | \([2]\) | \(330301440\) | \(4.6288\) | |
| 141120.gn1 | 141120ek4 | \([0, 0, 0, -180033840588, -29402166520305488]\) | \(229625675762164624948320008/9568125\) | \(26890107830046720000\) | \([2]\) | \(330301440\) | \(4.6288\) |
Rank
sage: E.rank()
The elliptic curves in class 141120ek have rank \(0\).
Complex multiplication
The elliptic curves in class 141120ek do not have complex multiplication.Modular form 141120.2.a.ek
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.
