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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 19110g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
19110.i2 | 19110g1 | \([1, 1, 0, -1432, 34336]\) | \(-6634840273369/6918968160\) | \(-339029439840\) | \([]\) | \(25920\) | \(0.90770\) | \(\Gamma_0(N)\)-optimal |
19110.i1 | 19110g2 | \([1, 1, 0, -136567, 19368469]\) | \(-5748703487739833929/1437696000\) | \(-70447104000\) | \([]\) | \(77760\) | \(1.4570\) |
Rank
sage: E.rank()
The elliptic curves in class 19110g have rank \(1\).
Complex multiplication
The elliptic curves in class 19110g do not have complex multiplication.Modular form 19110.2.a.g
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.