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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 2310a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2310.a3 | 2310a1 | \([1, 1, 0, -6958, -224588]\) | \(37262716093162729/333053952000\) | \(333053952000\) | \([2]\) | \(3840\) | \(1.0340\) | \(\Gamma_0(N)\)-optimal |
2310.a2 | 2310a2 | \([1, 1, 0, -12078, 143028]\) | \(194878967635813609/103306896000000\) | \(103306896000000\) | \([2, 2]\) | \(7680\) | \(1.3805\) | |
2310.a1 | 2310a3 | \([1, 1, 0, -152078, 22739028]\) | \(388980071198593573609/486165942108000\) | \(486165942108000\) | \([2]\) | \(15360\) | \(1.7271\) | |
2310.a4 | 2310a4 | \([1, 1, 0, 46002, 1176852]\) | \(10765621376623941911/6809085937500000\) | \(-6809085937500000\) | \([2]\) | \(15360\) | \(1.7271\) |
Rank
sage: E.rank()
The elliptic curves in class 2310a have rank \(1\).
Complex multiplication
The elliptic curves in class 2310a do not have complex multiplication.Modular form 2310.2.a.a
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.