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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 270802.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 270802.f1 | 270802f3 | \([1, -1, 0, -9717097916, 368685318380672]\) | \(170586815436843383543017473/2166416\) | \(1288634759787536\) | \([2]\) | \(129024000\) | \(3.8859\) | |
| 270802.f2 | 270802f4 | \([1, -1, 0, -608866076, 5729990140704]\) | \(41966336340198080824833/442001722607124848\) | \(262912932528890780348980208\) | \([2]\) | \(129024000\) | \(3.8859\) | |
| 270802.f3 | 270802f2 | \([1, -1, 0, -607318636, 5760821644752]\) | \(41647175116728660507393/4693358285056\) | \(2791718961759874590976\) | \([2, 2]\) | \(64512000\) | \(3.5393\) | |
| 270802.f4 | 270802f1 | \([1, -1, 0, -37860716, 90501352144]\) | \(-10090256344188054273/107965577101312\) | \(-64220443125083957297152\) | \([2]\) | \(32256000\) | \(3.1927\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 270802.f have rank \(0\).
Complex multiplication
The elliptic curves in class 270802.f do not have complex multiplication.Modular form 270802.2.a.f
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.
