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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 12075.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
12075.v1 | 12075s3 | \([1, 0, 1, -126276, 17260573]\) | \(14251520160844849/264449745\) | \(4132027265625\) | \([2]\) | \(46080\) | \(1.5457\) | |
12075.v2 | 12075s2 | \([1, 0, 1, -8151, 250573]\) | \(3832302404449/472410225\) | \(7381409765625\) | \([2, 2]\) | \(23040\) | \(1.1992\) | |
12075.v3 | 12075s1 | \([1, 0, 1, -2026, -31177]\) | \(58818484369/7455105\) | \(116486015625\) | \([2]\) | \(11520\) | \(0.85260\) | \(\Gamma_0(N)\)-optimal |
12075.v4 | 12075s4 | \([1, 0, 1, 11974, 1297073]\) | \(12152722588271/53476250625\) | \(-835566416015625\) | \([2]\) | \(46080\) | \(1.5457\) |
Rank
sage: E.rank()
The elliptic curves in class 12075.v have rank \(0\).
Complex multiplication
The elliptic curves in class 12075.v do not have complex multiplication.Modular form 12075.2.a.v
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.