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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 270480w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 270480.w2 | 270480w1 | \([0, -1, 0, -356981, 88942281]\) | \(-8185177630572544/808255330875\) | \(-496798988654304000\) | \([]\) | \(4665600\) | \(2.1362\) | \(\Gamma_0(N)\)-optimal |
| 270480.w1 | 270480w2 | \([0, -1, 0, -29568821, 61896813945]\) | \(-4651506434740759035904/3638671875\) | \(-2236531500000000\) | \([]\) | \(13996800\) | \(2.6855\) |
Rank
sage: E.rank()
The elliptic curves in class 270480w have rank \(0\).
Complex multiplication
The elliptic curves in class 270480w do not have complex multiplication.Modular form 270480.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
