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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 195195.q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 195195.q1 | 195195d3 | \([1, 0, 0, -3530504390, 80736117970767]\) | \(1008263082603610603475953129/90818848068071248125\) | \(438365233224598913090983125\) | \([2]\) | \(148635648\) | \(4.1518\) | |
| 195195.q2 | 195195d4 | \([1, 0, 0, -1289204420, -16921859324475]\) | \(49094060756434440524632009/2782940530242919921875\) | \(13432722397841298065185546875\) | \([2]\) | \(148635648\) | \(4.1518\) | |
| 195195.q3 | 195195d2 | \([1, 0, 0, -236588765, 1068815881392]\) | \(303421219916435677303129/73345189777625390625\) | \(354023222125350234097265625\) | \([2, 2]\) | \(74317824\) | \(3.8053\) | |
| 195195.q4 | 195195d1 | \([1, 0, 0, 35069440, 105135564975]\) | \(988211925316565164151/1561115353427004375\) | \(-7535205637959645560289375\) | \([4]\) | \(37158912\) | \(3.4587\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 195195.q have rank \(0\).
Complex multiplication
The elliptic curves in class 195195.q do not have complex multiplication.Modular form 195195.2.a.q
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
