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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 37905l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
37905.f3 | 37905l1 | \([1, 1, 1, -313670200, 2138110844360]\) | \(72547406094380206981321/240210178108425\) | \(11300899454277767647425\) | \([4]\) | \(7603200\) | \(3.4540\) | \(\Gamma_0(N)\)-optimal |
37905.f2 | 37905l2 | \([1, 1, 1, -318004005, 2075983149402]\) | \(75596184328076883820441/4168754598395480625\) | \(196122732754316572421555625\) | \([2, 2]\) | \(15206400\) | \(3.8005\) | |
37905.f4 | 37905l3 | \([1, 1, 1, 219299370, 8377906974102]\) | \(24792153857163653065559/658848518533019475675\) | \(-30996108999930728823288444675\) | \([2]\) | \(30412800\) | \(4.1471\) | |
37905.f1 | 37905l4 | \([1, 1, 1, -924648260, -8202026476510]\) | \(1858368248693819973741961/457764396920504296875\) | \(21535929343558811610769921875\) | \([2]\) | \(30412800\) | \(4.1471\) |
Rank
sage: E.rank()
The elliptic curves in class 37905l have rank \(0\).
Complex multiplication
The elliptic curves in class 37905l do not have complex multiplication.Modular form 37905.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.