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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 364650.q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 364650.q1 | 364650q6 | \([1, 1, 0, -15877950124875, -24329681454238621875]\) | \(28332636278699790163698668543341945468081/30435816720023658978554624568750000\) | \(475559636250369671539916008886718750000\) | \([2]\) | \(26046627840\) | \(6.3375\) | |
| 364650.q2 | 364650q3 | \([1, 1, 0, -11096407350875, 14227268256867268125]\) | \(9670542997417555153739805666603463800241/1011632472308222823279605978880\) | \(15806757379815981613743843420000000\) | \([2]\) | \(13023313920\) | \(5.9909\) | |
| 364650.q3 | 364650q4 | \([1, 1, 0, -1241313142875, -174736986385147875]\) | \(13537789194164358932476757607878858161/6990196961633622849153431264160000\) | \(109221827525525357018022363502500000000\) | \([2, 2]\) | \(13023313920\) | \(5.9909\) | |
| 364650.q4 | 364650q2 | \([1, 1, 0, -695227990875, 221154543664228125]\) | \(2378402942216976240269041980443870641/24141832888458098359553295974400\) | \(377216138882157786868020249600000000\) | \([2, 2]\) | \(6511656960\) | \(5.6444\) | |
| 364650.q5 | 364650q1 | \([1, 1, 0, -11023958875, 8495035866212125]\) | \(-9482360001398682199577266111921/1989750139832011668270329364480\) | \(-31089845934875182316723896320000000\) | \([2]\) | \(3255828480\) | \(5.2978\) | \(\Gamma_0(N)\)-optimal |
| 364650.q6 | 364650q5 | \([1, 1, 0, 4657961407125, -1356839519988697875]\) | \(715305136889332363556605654855198869839/464850218389561926618649625559572400\) | \(-7263284662336905103416400399368318750000\) | \([2]\) | \(26046627840\) | \(6.3375\) |
Rank
sage: E.rank()
The elliptic curves in class 364650.q have rank \(1\).
Complex multiplication
The elliptic curves in class 364650.q do not have complex multiplication.Modular form 364650.2.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.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 8 & 4 \\ 8 & 1 & 4 & 2 & 4 & 8 \\ 2 & 4 & 1 & 2 & 4 & 2 \\ 4 & 2 & 2 & 1 & 2 & 4 \\ 8 & 4 & 4 & 2 & 1 & 8 \\ 4 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
