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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 68970.z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 68970.z1 | 68970r2 | \([1, 0, 1, -18460654, -30526102444]\) | \(522741368615530635369539/96458757887812500\) | \(128386606748678437500\) | \([2]\) | \(6193152\) | \(2.8610\) | |
| 68970.z2 | 68970r1 | \([1, 0, 1, -1273154, -372352444]\) | \(171469934851410369539/54255761718750000\) | \(72214418847656250000\) | \([2]\) | \(3096576\) | \(2.5145\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 68970.z have rank \(0\).
Complex multiplication
The elliptic curves in class 68970.z do not have complex multiplication.Modular form 68970.2.a.z
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
