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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 56112.u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 56112.u1 | 56112bc4 | \([0, 1, 0, -3492944, 2511446676]\) | \(1150638118585800835537/31752757008504\) | \(130059292706832384\) | \([4]\) | \(1548288\) | \(2.3870\) | |
| 56112.u2 | 56112bc3 | \([0, 1, 0, -975184, -335507308]\) | \(25039399590518087377/2641281025170312\) | \(10818687079097597952\) | \([2]\) | \(1548288\) | \(2.3870\) | |
| 56112.u3 | 56112bc2 | \([0, 1, 0, -227024, 35879316]\) | \(315922815546536017/46479778841664\) | \(190381174135455744\) | \([2, 2]\) | \(774144\) | \(2.0405\) | |
| 56112.u4 | 56112bc1 | \([0, 1, 0, 23856, 3064212]\) | \(366554400441263/1197281046528\) | \(-4904063166578688\) | \([2]\) | \(387072\) | \(1.6939\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 56112.u have rank \(0\).
Complex multiplication
The elliptic curves in class 56112.u do not have complex multiplication.Modular form 56112.2.a.u
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.
