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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 12495.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
12495.l1 | 12495l2 | \([1, 0, 1, -3799, 89471]\) | \(51520374361/212415\) | \(24990412335\) | \([2]\) | \(12288\) | \(0.85052\) | |
12495.l2 | 12495l1 | \([1, 0, 1, -124, 2741]\) | \(-1771561/26775\) | \(-3150051975\) | \([2]\) | \(6144\) | \(0.50395\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 12495.l have rank \(0\).
Complex multiplication
The elliptic curves in class 12495.l do not have complex multiplication.Modular form 12495.2.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 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.