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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 12600.q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 12600.q1 | 12600l4 | \([0, 0, 0, -840675, 296680750]\) | \(5633270409316/14175\) | \(165337200000000\) | \([2]\) | \(98304\) | \(1.9665\) | |
| 12600.q2 | 12600l3 | \([0, 0, 0, -147675, -15988250]\) | \(30534944836/8203125\) | \(95681250000000000\) | \([2]\) | \(98304\) | \(1.9665\) | |
| 12600.q3 | 12600l2 | \([0, 0, 0, -53175, 4518250]\) | \(5702413264/275625\) | \(803722500000000\) | \([2, 2]\) | \(49152\) | \(1.6199\) | |
| 12600.q4 | 12600l1 | \([0, 0, 0, 1950, 273625]\) | \(4499456/180075\) | \(-32818668750000\) | \([2]\) | \(24576\) | \(1.2734\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 12600.q have rank \(0\).
Complex multiplication
The elliptic curves in class 12600.q do not have complex multiplication.Modular form 12600.2.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.
