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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 247962.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
247962.f1 | 247962f3 | \([1, 1, 0, -952318730, -11310025748268]\) | \(3957101249824708884951625/772310238681366528\) | \(18641691675577953583890432\) | \([2]\) | \(131383296\) | \(3.8487\) | |
247962.f2 | 247962f4 | \([1, 1, 0, -851700490, -13793102798636]\) | \(-2830680648734534916567625/1766676274677722124288\) | \(-42643270480696470537828175872\) | \([2]\) | \(262766592\) | \(4.1952\) | |
247962.f3 | 247962f1 | \([1, 1, 0, -28994075, 38899354269]\) | \(111675519439697265625/37528570137307392\) | \(905848451160596648610048\) | \([2]\) | \(43794432\) | \(3.2994\) | \(\Gamma_0(N)\)-optimal |
247962.f4 | 247962f2 | \([1, 1, 0, 84594485, 268961623693]\) | \(2773679829880629422375/2899504554614368272\) | \(-69986991252818582556810768\) | \([2]\) | \(87588864\) | \(3.6459\) |
Rank
sage: E.rank()
The elliptic curves in class 247962.f have rank \(0\).
Complex multiplication
The elliptic curves in class 247962.f do not have complex multiplication.Modular form 247962.2.a.f
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.