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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 1584l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1584.h3 | 1584l1 | \([0, 0, 0, -795, 8138]\) | \(18609625/1188\) | \(3547348992\) | \([2]\) | \(768\) | \(0.58307\) | \(\Gamma_0(N)\)-optimal |
1584.h4 | 1584l2 | \([0, 0, 0, 645, 34346]\) | \(9938375/176418\) | \(-526781325312\) | \([2]\) | \(1536\) | \(0.92964\) | |
1584.h1 | 1584l3 | \([0, 0, 0, -11595, -478726]\) | \(57736239625/255552\) | \(763074183168\) | \([2]\) | \(2304\) | \(1.1324\) | |
1584.h2 | 1584l4 | \([0, 0, 0, -5835, -954502]\) | \(-7357983625/127552392\) | \(-380869401673728\) | \([2]\) | \(4608\) | \(1.4790\) |
Rank
sage: E.rank()
The elliptic curves in class 1584l have rank \(1\).
Complex multiplication
The elliptic curves in class 1584l do not have complex multiplication.Modular form 1584.2.a.l
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.