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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 81120w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 81120.bt2 | 81120w1 | \([0, 1, 0, -332310, -88923600]\) | \(-13137573612736/3427734375\) | \(-1058881224375000000\) | \([2]\) | \(967680\) | \(2.1756\) | \(\Gamma_0(N)\)-optimal |
| 81120.bt1 | 81120w2 | \([0, 1, 0, -5613560, -5120898600]\) | \(7916055336451592/385003125\) | \(951468312974400000\) | \([2]\) | \(1935360\) | \(2.5222\) |
Rank
sage: E.rank()
The elliptic curves in class 81120w have rank \(1\).
Complex multiplication
The elliptic curves in class 81120w do not have complex multiplication.Modular form 81120.2.a.w
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
