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SageMath
E = EllipticCurve("hb1")
E.isogeny_class()
Elliptic curves in class 103488.hb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 103488.hb1 | 103488ds3 | \([0, 1, 0, -252513, 48568575]\) | \(57736239625/255552\) | \(7881473981939712\) | \([2]\) | \(829440\) | \(1.9026\) | |
| 103488.hb2 | 103488ds4 | \([0, 1, 0, -127073, 96963327]\) | \(-7357983625/127552392\) | \(-3933840701235658752\) | \([2]\) | \(1658880\) | \(2.2492\) | |
| 103488.hb3 | 103488ds1 | \([0, 1, 0, -17313, -832833]\) | \(18609625/1188\) | \(36639083593728\) | \([2]\) | \(276480\) | \(1.3533\) | \(\Gamma_0(N)\)-optimal |
| 103488.hb4 | 103488ds2 | \([0, 1, 0, 14047, -3485889]\) | \(9938375/176418\) | \(-5440903913668608\) | \([2]\) | \(552960\) | \(1.6999\) |
Rank
sage: E.rank()
The elliptic curves in class 103488.hb have rank \(0\).
Complex multiplication
The elliptic curves in class 103488.hb do not have complex multiplication.Modular form 103488.2.a.hb
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
