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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 111573.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
111573.i1 | 111573bi2 | \([1, -1, 1, -1053844112, 13168046841940]\) | \(4399901392374538640127/64009\) | \(1883002648207527\) | \([2]\) | \(35782656\) | \(3.4140\) | |
111573.i2 | 111573bi1 | \([1, -1, 1, -65865197, 205763477140]\) | \(-1074191725926252207/4097152081\) | \(-120529116509115595743\) | \([2]\) | \(17891328\) | \(3.0674\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 111573.i have rank \(0\).
Complex multiplication
The elliptic curves in class 111573.i do not have complex multiplication.Modular form 111573.2.a.i
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.