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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 145656.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 145656.f1 | 145656e3 | \([0, 0, 0, -1415811, 589314350]\) | \(17418812548/1753941\) | \(31603559036901110784\) | \([2]\) | \(2949120\) | \(2.4778\) | |
| 145656.f2 | 145656e2 | \([0, 0, 0, -323391, -60675550]\) | \(830321872/127449\) | \(574113096691110144\) | \([2, 2]\) | \(1474560\) | \(2.1312\) | |
| 145656.f3 | 145656e1 | \([0, 0, 0, -310386, -66556411]\) | \(11745974272/357\) | \(100509995919312\) | \([2]\) | \(737280\) | \(1.7846\) | \(\Gamma_0(N)\)-optimal |
| 145656.f4 | 145656e4 | \([0, 0, 0, 560949, -334290346]\) | \(1083360092/3306177\) | \(-59572676621359899648\) | \([2]\) | \(2949120\) | \(2.4778\) |
Rank
sage: E.rank()
The elliptic curves in class 145656.f have rank \(1\).
Complex multiplication
The elliptic curves in class 145656.f do not have complex multiplication.Modular form 145656.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
